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Yaz kampı kapsamında EBOB (En Büyük Ortak Bölen) konusundaki problemleri çözmektedir.","Videoda, 9'dan 14'e kadar olan EBOB problemleri adım adım çözülmektedir. Öğretmen, ardışık sayıların EBOB'unun 1 olduğunu, birbirinin katı olan sayıların EBOB'unun küçük olan sayı olduğunu ve çeşitli uygulamalı problemleri (kütük kesme, çiftçinin yem çuvallarını paylaşması, aydınlatma direkleri yerleştirme, fayans yerleştirme ve tarlalarda fidan dikme) EBOB kavramı kullanarak çözmektedir.","Her problem için detaylı çözüm adımları ve hesaplamalar sunulmakta, farklı çözüm yöntemleri gösterilmektedir. Video, bir sonraki videoda görüşmek üzere sonlanmaktadır."]},"endTime":1081,"title":"EBOB Problemleri Çözüm Videosu","beginTime":0}],"fullResult":[{"index":0,"title":"EBOB Sorularının Çözümü","list":{"type":"unordered","items":["Yaz kampının 15. videosunda 9'dan 16'ya kadar olan EBOB soruları çözülecektir.","Önceki videoda 1'den 8'e kadar olan EBOB soruları çözülmüştü.","Soruları çözmeden izleyenler için açıklama kısmında PDF dosyasının linki bulunmaktadır."]},"beginTime":1,"endTime":30,"href":"/video/preview/16245020189150668789?parent-reqid=1769174491020420-11708332147746153643-balancer-l7leveler-kubr-yp-klg-160-BAL&text=15problemzzzz&t=1&ask_summarization=1"},{"index":1,"title":"9. 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Soru Çözümü","list":{"type":"unordered","items":["960 metre ve 600 metre uzunluğundaki iki yolda, başlangıç ve bitişlerine de yerleştirilecek aydınlatma direkleri için en az sayıda direk için yapılan yerleştirme işlemi incelenmiştir.","İki sayının EBOB'u 120 olduğundan, 960 metrelik yolda 9, 600 metrelik yolda 6 direk olur.","Toplam 15 direk yerleştirilir."]},"beginTime":295,"endTime":537,"href":"/video/preview/16245020189150668789?parent-reqid=1769174491020420-11708332147746153643-balancer-l7leveler-kubr-yp-klg-160-BAL&text=15problemzzzz&t=295&ask_summarization=1"},{"index":5,"title":"13. Soru Çözümü","list":{"type":"unordered","items":["ABC harflerinin her biri, bağlı olduğu iki sayının EBOB'una eşittir.","A=9, B=15, C=3 olarak bulunur ve A+B+C=27 olarak hesaplanır."]},"beginTime":537,"endTime":660,"href":"/video/preview/16245020189150668789?parent-reqid=1769174491020420-11708332147746153643-balancer-l7leveler-kubr-yp-klg-160-BAL&text=15problemzzzz&t=537&ask_summarization=1"},{"index":6,"title":"14. 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dikilebilir."]},"beginTime":714,"endTime":783,"href":"/video/preview/16245020189150668789?parent-reqid=1769174491020420-11708332147746153643-balancer-l7leveler-kubr-yp-klg-160-BAL&text=15problemzzzz&t=714&ask_summarization=1"},{"index":8,"title":"Alternatif Çözüm Yöntemi","list":{"type":"unordered","items":["Algoritmada sadece ortak bölenleri kullanarak çözüm yapılabilir.","Kısa kenara 24, uzun kenara 31 fidan dikilir ve toplam 55 fidan bulunur.","Alternatif çözümde en altta çıkan sayılarla da cevap bulunabilir."]},"beginTime":783,"endTime":820,"href":"/video/preview/16245020189150668789?parent-reqid=1769174491020420-11708332147746153643-balancer-l7leveler-kubr-yp-klg-160-BAL&text=15problemzzzz&t=783&ask_summarization=1"},{"index":9,"title":"Sayılar Problemi","list":{"type":"unordered","items":["İki sayıdan biri diğerinin beş katı olduğunda, biri a ise diğeri 5a olur.","Her iki sayı da a'ya bölünebilir.","Bu iki sayının toplamı 6a 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Matematiğin en önemli bölümü sınav kazandıran yeri Problemler. Problemleri adım adım bitiriyoruz. Problemler 15 dersimizde Hareket Hız Problemleri 2 konu anlatım ve soru çözümü yapıyoruz.","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/3371183/97054fb367c0330e0a15562592bd8ef5/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/nrLZ0wEAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"2","reqid":"1769174491020420-11708332147746153643-balancer-l7leveler-kubr-yp-klg-160-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1769174491020420-11708332147746153643-balancer-l7leveler-kubr-yp-klg-160-BAL&text=videoid:16603614400766535229","teaser":[{"list":{"type":"unordered","items":["Bu video, bir eğitmen tarafından sunulan \"Problemlerin Problem Olmaktan Çıktığı Problemler Kampı\" kapsamında hareket problemleri konusunu ele alan bir eğitim içeriğidir. Eğitmen, öğrencilere hitap ederek problem çözme yöntemlerini adım adım anlatmaktadır.","Videoda mum problemleri, hız-zaman-yol ilişkisi, oran-orantı ve geometri problemleri gibi çeşitli hareket problemleri ele alınmaktadır. Eğitmen, her problem türünü farklı örneklerle açıklamakta, şekil çizerek çözüm sürecini görselleştirmekte ve \"yol = hız × zaman\" formülünü kullanarak detaylı çözüm yöntemlerini göstermektedir.","Video, 17 sayfalık bir ders serisinin 14. adımını oluşturmaktadır ve son bölümde konum-zaman grafiği üzerinden hız hesaplamaları, karşılaşma ve arkadan yetişme problemlerini içermektedir. Matematik sınavlarına hazırlanan öğrenciler için faydalı problem çözme teknikleri sunan bu içerik, ezber yerine işin mantığını anlamayı amaçlamaktadır."]},"endTime":2721,"title":"Hareket Problemleri Eğitim Videosu","beginTime":0}],"fullResult":[{"index":0,"title":"Problemlerle Mücadele","list":{"type":"unordered","items":["Problemlerin problem olmaktan çıktığı problemler kampına kaldığımız yerden devam ediyoruz.","Problemleri yapmaktan vazgeçmek sınavdan vazgeçmek demektir, bu yüzden vazgeçmemek gerekir.","Sınav günü geldiğinde \"elimden gelenin hepsini yaptım\" diyebilmek için çalışmak önemlidir."]},"beginTime":0,"endTime":63,"href":"/video/preview/16603614400766535229?parent-reqid=1769174491020420-11708332147746153643-balancer-l7leveler-kubr-yp-klg-160-BAL&text=15problemzzzz&t=0&ask_summarization=1"},{"index":1,"title":"Hareket Problemleri","list":{"type":"unordered","items":["Hareket problemlerinin üçüncüsündeyiz ve on iki adım hareket problemlerinin son dersindeyiz.","Mum problemleri hız problemlerinden farklıdır, ancak yol problemiyle aynı mantıkla çözülür.","Mumlar yol gibidir ve aynı yerden başlayıp aynı yerde biterler."]},"beginTime":63,"endTime":92,"href":"/video/preview/16603614400766535229?parent-reqid=1769174491020420-11708332147746153643-balancer-l7leveler-kubr-yp-klg-160-BAL&text=15problemzzzz&t=63&ask_summarization=1"},{"index":2,"title":"Mum Problemi Çözümü","list":{"type":"unordered","items":["Boyları eşit iki mumdan biri üç saatte, diğeri beş saatte yanıp bitiyor.","Hızlar arasında oran kurulur: birinci mumun hızı v₁, ikinci mumun hızı 3v₁ olur.","Bir mumun boyu diğerinin boyunun iki katı olacak şekilde 15/7 saat sonra olur."]},"beginTime":92,"endTime":280,"href":"/video/preview/16603614400766535229?parent-reqid=1769174491020420-11708332147746153643-balancer-l7leveler-kubr-yp-klg-160-BAL&text=15problemzzzz&t=92&ask_summarization=1"},{"index":3,"title":"İkinci Mum Problemi","list":{"type":"unordered","items":["Boyları eşit iki mumdan biri iki saatte, diğeri beş saatte yanıp bitiyor.","Hızlar arasında ters orantı kurulur: birinci mumun hızı 5v₁, ikinci mumun hızı 2v₁ olur.","Bir mumun boyu diğerinin boyunun üçte biri olacak şekilde 20/13 saat sonra olur."]},"beginTime":280,"endTime":452,"href":"/video/preview/16603614400766535229?parent-reqid=1769174491020420-11708332147746153643-balancer-l7leveler-kubr-yp-klg-160-BAL&text=15problemzzzz&t=280&ask_summarization=1"},{"index":4,"title":"Mum Problemi Çözümü","list":{"type":"unordered","items":["İki farklı yapıdaki mumların boyları sırasıyla 2 ve 3 ile orantılıdır, yani birinin boyu 2k, diğerinin boyu 3k'dir.","Kısa olan mum 5 saatte, uzun olan mum 3 saatte tamamen yanıp bitiyor.","Hızları oranı v₂/v₁ = 5/2 olarak hesaplanmıştır."]},"beginTime":454,"endTime":546,"href":"/video/preview/16603614400766535229?parent-reqid=1769174491020420-11708332147746153643-balancer-l7leveler-kubr-yp-klg-160-BAL&text=15problemzzzz&t=454&ask_summarization=1"},{"index":5,"title":"Mumların Boylarının Eşit Olması","list":{"type":"unordered","items":["İki mum aynı anda yakıldıktan 2 saat sonra uzun mum sönüyor, kısa mum yanmaya devam ediyor.","2 saat sonunda uzun mumun kalan boyu 3k-10v, kısa mumun kalan boyu 2k-4v olarak hesaplanmıştır.","Kısa mum kaç saat daha yanarsa mumların boyları eşit olur sorusunun cevabı 1,5 saat olarak bulunmuştur."]},"beginTime":546,"endTime":756,"href":"/video/preview/16603614400766535229?parent-reqid=1769174491020420-11708332147746153643-balancer-l7leveler-kubr-yp-klg-160-BAL&text=15problemzzzz&t=546&ask_summarization=1"},{"index":6,"title":"Hızları Oranı Problemi","list":{"type":"unordered","items":["Hızları oranı verildiğinde v₁/v₂ = a/b ise v₁a × v₂b = v şeklinde taraf tarafa oranlanabilir.","CD 40 km uzunluğunda, hızları oranı 3/4 olan iki araç aynı anda birbirlerine doğru hareket ediyor ve C noktasında karşılaşıyorlar.","AB yolunun tamamı 280 km olarak hesaplanmıştır."]},"beginTime":756,"endTime":868,"href":"/video/preview/16603614400766535229?parent-reqid=1769174491020420-11708332147746153643-balancer-l7leveler-kubr-yp-klg-160-BAL&text=15problemzzzz&t=756&ask_summarization=1"},{"index":7,"title":"Hız Problemi Çözümü","list":{"type":"unordered","items":["A, B ve C noktaları arasında, A ve B noktaları x birim uzunluğunda, BC uzunluğu 3x birim uzunluğundadır.","İki araç, biri B'den A'ya, diğeri B'den C'ye doğru hareket ediyor; A noktasına gelen araç durmadan C'ye geri dönüyor ve diğer araç C noktasında onu yakalıyor.","V1 ve V2 hızları arasındaki oran 5/3 olarak hesaplanıyor."]},"beginTime":871,"endTime":959,"href":"/video/preview/16603614400766535229?parent-reqid=1769174491020420-11708332147746153643-balancer-l7leveler-kubr-yp-klg-160-BAL&text=15problemzzzz&t=871&ask_summarization=1"},{"index":8,"title":"İki Araç Hız Problemi","list":{"type":"unordered","items":["İki araç aynı anda A noktasından C'ye doğru yola çıkıyor; biri sabit hızla asfalt yoldan, diğeri önce çakıl yolda %20, sonra toprak yolda %20 azaltarak C'ye varıyor.","Yolun tamamı 200 km olup, CD/AB oranı 1/4'tür; bu oran 40 km olarak hesaplanıyor.","Sabit hızla giden araç 28/5 saat (336 dakika) içinde C'ye varırken, hız azaltan araç 21/4 saat (315 dakika) içinde varıyor ve aradaki fark 21 dakika olarak bulunuyor."]},"beginTime":959,"endTime":1257,"href":"/video/preview/16603614400766535229?parent-reqid=1769174491020420-11708332147746153643-balancer-l7leveler-kubr-yp-klg-160-BAL&text=15problemzzzz&t=959&ask_summarization=1"},{"index":9,"title":"Yarışmacı Problemlerinde Temel Prensip","list":{"type":"unordered","items":["Bilgi cümlesinin hareketleri, hızları ve oranını anlattığı fark edilmelidir.","Yarışmacı sorularında şekil çizmek hayat kurtarır.","Örneklerde birinci yarışmacı 250 metre, ikinci yarışmacı 225 metre, üçüncü yarışmacı 180 metre yol almıştır."]},"beginTime":1260,"endTime":1314,"href":"/video/preview/16603614400766535229?parent-reqid=1769174491020420-11708332147746153643-balancer-l7leveler-kubr-yp-klg-160-BAL&text=15problemzzzz&t=1260&ask_summarization=1"},{"index":10,"title":"İlk Örnek Çözümü","list":{"type":"unordered","items":["İkinci yarışmacı koşuyu tamamladığında, üçüncü yarışmacının bitirmesi için 50 metre kalmıştır.","İkinci yarışmacı 225 metre yol alırken 45 metre fark atıyorsa, 250 metre yol alırsa 50 metre fark atacaktır.","Bu problem oran orantı sorusundan başka bir şey değildir."]},"beginTime":1314,"endTime":1414,"href":"/video/preview/16603614400766535229?parent-reqid=1769174491020420-11708332147746153643-balancer-l7leveler-kubr-yp-klg-160-BAL&text=15problemzzzz&t=1314&ask_summarization=1"},{"index":11,"title":"İkinci Örnek Çözümü","list":{"type":"unordered","items":["Şakir yarışı bitirmesine 100 metre kaldığında, Necati'nin 150 metresi kalmıştır.","Şakir yarışı bitirdiğinde, Necati'nin bitirmesi için 60 metre kalmıştır.","Yarış parkuru 600 metre olarak hesaplanmıştır."]},"beginTime":1414,"endTime":1556,"href":"/video/preview/16603614400766535229?parent-reqid=1769174491020420-11708332147746153643-balancer-l7leveler-kubr-yp-klg-160-BAL&text=15problemzzzz&t=1414&ask_summarization=1"},{"index":12,"title":"Üçüncü Örnek Sorusu","list":{"type":"unordered","items":["Birinci yarışmacı koşuyu ikinci yarışmacının 1000 metre, üçüncü yarışmacının 1200 metre önünde tamamlamıştır.","Birinci yarışmacı vardığında, ikinci yarışmacının 1000 metre önünde, üçüncü yarışmacının 1200 metre önündeymiş.","Birinci yarışmacı koşuyu tamamladığında, üçüncü yarışmacının hızını iki katına çıkarıyor ve ikinci yarışmacının 100 metre önünde tamamlıyor."]},"beginTime":1556,"endTime":1625,"href":"/video/preview/16603614400766535229?parent-reqid=1769174491020420-11708332147746153643-balancer-l7leveler-kubr-yp-klg-160-BAL&text=15problemzzzz&t=1556&ask_summarization=1"},{"index":13,"title":"Yarışmacılar 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Eğitmen, öğrencilere matematik ve mantık sorularını adım adım çözerek anlatmaktadır.","Videoda toplam on soru çözülmektedir. İçerikte doğru orantı problemleri, grafik soruları, sayısal mantık problemleri, denklem çözme teknikleri ve hız-zaman problemleri ele alınmaktadır. Eğitmen, her soruyu detaylı olarak açıklamakta ve çözüm stratejilerini göstermektedir.","Dersin sonunda eğitmen, sınavlara hazırlık için toplam 5-6 ders yapacaklarını ve sonrasında deneme sınavları çözeceklerini belirtmektedir. Video, ÖSYM formatında sorular çözerek öğrencilere sınav hazırlığı için yardımcı olmayı amaçlamaktadır."]},"endTime":2233,"title":"ÖSYM Mantık ve Matematik Soruları Çözüm Dersi","beginTime":0}],"fullResult":[{"index":0,"title":"Dersin İçeriği ve Planı","list":{"type":"unordered","items":["Eğitmen, abone olmayanların dersi anlamayacağını belirtiyor.","On soru çözeceğini, ancak problem soruları da koyacağını söylüyor.","Geçen hafta problem rehberliği yapmış olduğunu ve bu derste zorlanılacak soruları çözeceğini belirtiyor."]},"beginTime":8,"endTime":57,"href":"/video/preview/13885020562927691415?parent-reqid=1769174491020420-11708332147746153643-balancer-l7leveler-kubr-yp-klg-160-BAL&text=15problemzzzz&t=8&ask_summarization=1"},{"index":1,"title":"Dersin İçeriği","list":{"type":"unordered","items":["Dersin içeriğinde beş soru, bir grafik sorusu ve üç sayısal mantık sorusu olacak.","Eğitmen, doğru orantı konusunun son yıllarda çıkan en önemli soru çeşitlerinden biri olduğunu vurguluyor.","Doğru orantı probleminde k1 ve k2 gibi değişkenler kullanıldığını açıklıyor."]},"beginTime":57,"endTime":155,"href":"/video/preview/13885020562927691415?parent-reqid=1769174491020420-11708332147746153643-balancer-l7leveler-kubr-yp-klg-160-BAL&text=15problemzzzz&t=57&ask_summarization=1"},{"index":2,"title":"Matematik Dersinin Amacı","list":{"type":"unordered","items":["Derslerin amacı soru çözüp geçmek değil, öğrencilere konuyu anlatmak ve anlamalarını sağlamaktır.","Öğretmen, soruları çözerken uzun süre konuşmakta ve öğrencilerin soruyu anlamaları için detaylı açıklamalar yapmaktadır."]},"beginTime":159,"endTime":181,"href":"/video/preview/13885020562927691415?parent-reqid=1769174491020420-11708332147746153643-balancer-l7leveler-kubr-yp-klg-160-BAL&text=15problemzzzz&t=159&ask_summarization=1"},{"index":3,"title":"Matematik Problemi Çözümü","list":{"type":"unordered","items":["Bir matematik problemi çözülürken, k₁ ve k₂ arasındaki ilişki bulunarak k₁=8x ve k₂=5x şeklinde 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paketlenmediği toplam paket sayısı 30.","Kampanya için hazırlanan paketlerden en az bir beyaz gömlek olan paket sayısı 18'dir."]},"beginTime":704,"endTime":936,"href":"/video/preview/13885020562927691415?parent-reqid=1769174491020420-11708332147746153643-balancer-l7leveler-kubr-yp-klg-160-BAL&text=15problemzzzz&t=704&ask_summarization=1"},{"index":7,"title":"Veri Grubu ve Açıklık Problemi","list":{"type":"unordered","items":["Veri grubu, sayıların olduğu grup demektir ve en büyük sayı ile en küçük sayı arasındaki farka açıklığı denir.","Kadrosu 20 oyuncudan oluşan bir takımın forma numaraları 1'den 20'ye kadar numaralandırılmıştır.","Oyundan çıkan oyuncunun forma numarası 4, oyuna giren oyuncunun forma numarası 15'tir ve bu oyuncuların forma numaraları toplamı 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çarpanlarına ayrılarak çözüm yapılır.","360 sayısı asal çarpanlarına ayrıldığında 2³×3²×5¹ olarak bulunur ve tabloya yerleştirildiğinde pozitif bölen sayısı 24 olarak hesaplanır.","Sayısal mantık sorularını çözmek için önce soruyu anlamak ve doğru şekilde yorumlamak önemlidir."]},"beginTime":1952,"endTime":2187,"href":"/video/preview/13885020562927691415?parent-reqid=1769174491020420-11708332147746153643-balancer-l7leveler-kubr-yp-klg-160-BAL&text=15problemzzzz&t=1952&ask_summarization=1"},{"index":13,"title":"Ders Planı","list":{"type":"unordered","items":["Dersler 40-45 dakika sürmekte ve 10 soru yeterli olmaktadır.","Sınava kadar 5-6 ders yapılacağı ve sonrasında genel deneme çözüleceği belirtilmektedir.","\"Yalnız Değilsin\" serisinde 4 tane temel 15 soruluk deneme çekildiği ve Ankara'da 14 tane problem denemesi çekileceği 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Eğitmen, fener şarjı, çay makinesi su miktarı, kitap basım ücreti, yaş çay satışları, elbise indirimleri, sucuk satışları, hatalı terazi ile baklava satışıyla ilgili kar hesaplaması, enflasyon ve alım gücü ile ilgili problem, bisiklet satışıyla ilgili denklem sistemi problemi gibi günlük hayattan örneklerle matematik problemlerini adım adım çözmektedir.","Video, \"Denizli\" olarak belirtilen bir yerde sona ermektedir ve matematik problemlerinin nasıl çözüleceğini öğrenmek isteyenler için faydalı bir kaynaktır."]},"endTime":1582,"title":"Matematik Problemleri Çözüm Dersi","beginTime":0}],"fullResult":[{"index":0,"title":"Yüzde Problemleri Soru Çözümü","list":{"type":"unordered","items":["Olağanüstü problemler kitabının soru çözümüne devam ediliyor ve yüzde kar zarar üç ve dört testi çözülecek.","İlk soruda şarj olan bir fenerin yüzde seksenbeş doluyken on dakikada tamamen şarj olduğu bilgisi veriliyor.","Fenerin şarjı yüzde altı iken şarja takılıp, yüzde yetmişsekiz doluluğa ulaştığında 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ediyor."]},"beginTime":635,"endTime":795,"href":"/video/preview/2214699495791673892?parent-reqid=1769174491020420-11708332147746153643-balancer-l7leveler-kubr-yp-klg-160-BAL&text=15problemzzzz&t=635&ask_summarization=1"},{"index":8,"title":"Enflasyon Problemi","list":{"type":"unordered","items":["Enflasyon, bir ürüne yapılan zam olarak algılanabilir.","Enflasyon yüzde altı olduğunda, yüz liralık bir ürün sene sonra yüzaltı lira olacak.","Memur maaşına bir hafta yüzde dört zam yapıldığında, ikinci altı ayda yüzde altı zam yapıldığında, alım gücü yüzde dört artıyor."]},"beginTime":795,"endTime":883,"href":"/video/preview/2214699495791673892?parent-reqid=1769174491020420-11708332147746153643-balancer-l7leveler-kubr-yp-klg-160-BAL&text=15problemzzzz&t=795&ask_summarization=1"},{"index":9,"title":"Bisiklet Satış Problemi","list":{"type":"unordered","items":["Bir kişi bisikleti üç x TL'ye aldı ve yüzde otuz karla satmayı planlıyor.","Bisikletin satış fiyatı üzerinden yüzde yirmi indirim 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Video, 15. soru tipinin çözümüyle başlayıp, 16. soru tipine geçiş yaparak sona ermektedir."]},"endTime":684,"title":"Matematik Öğretmeni Mustafa Güler'in Terazilerle İlgili Problemler Dersi","beginTime":0}],"fullResult":[{"index":0,"title":"Terazi Problemleri Giriş","list":{"type":"unordered","items":["Matematik öğretmeni Mustafa Güler, sayı ve genel yetenek problemlerinden 15. soru tipine giriş yapıyor.","Toplamda şimdiye kadar üç tane benzer soru tarzı çıkmış ve 2018 yılındaki sorular da buna benzerdi."]},"beginTime":0,"endTime":25,"href":"/video/preview/4915354905333891951?parent-reqid=1769174491020420-11708332147746153643-balancer-l7leveler-kubr-yp-klg-160-BAL&text=15problemzzzz&t=0&ask_summarization=1"},{"index":1,"title":"Terazi Dengesi Problemi","list":{"type":"unordered","items":["A terazisinde iki topa 45 gramlık ağırlık var ve dengede.","B kefesine bir ağırlık alınıp diğer tarafa aktarıldığında, aktarılan ağırlığın iki katı olmalı.","Örnek olarak 40 gram ve 20 gram ağırlıkların iki katı olan 60 gram ve 100 gram ağırlıkların dengede olduğu gösteriliyor."]},"beginTime":25,"endTime":85,"href":"/video/preview/4915354905333891951?parent-reqid=1769174491020420-11708332147746153643-balancer-l7leveler-kubr-yp-klg-160-BAL&text=15problemzzzz&t=25&ask_summarization=1"},{"index":2,"title":"Terazi Dengesi Problemi Çözümü","list":{"type":"unordered","items":["Sol ve sağ kefeler dengede, sağ kefesine x gramlık bir ağırlık alınıyor.","Bir ağırlık diğer tarafa aktarıldığında, aktarılan ağırlığın iki katı olmalı.","Örnek olarak 60 gram ve 30 gram ağırlıkların iki katı olan 80 gram ve 65 gram ağırlıkların dengede olduğu gösteriliyor."]},"beginTime":85,"endTime":157,"href":"/video/preview/4915354905333891951?parent-reqid=1769174491020420-11708332147746153643-balancer-l7leveler-kubr-yp-klg-160-BAL&text=15problemzzzz&t=85&ask_summarization=1"},{"index":3,"title":"Terazi Problemi Çözümü","list":{"type":"unordered","items":["Sağ ve sol kefe tablet için verilmiş, hep sol kefe ağırlık geliyor.","x+z+2x+z+2t>0 eşitsizliği alt alta toplanarak t>y sonucuna ulaşılıyor.","Üçünün kütleleri eşit, farklı olan t ise x ve z'ye eşittir."]},"beginTime":157,"endTime":344,"href":"/video/preview/4915354905333891951?parent-reqid=1769174491020420-11708332147746153643-balancer-l7leveler-kubr-yp-klg-160-BAL&text=15problemzzzz&t=157&ask_summarization=1"},{"index":4,"title":"Terazi Problemi Çözümü","list":{"type":"unordered","items":["İki kefede 13 kg ve 11 kg ağırlıklar var, çarpımları birbirine eşit olacak şekilde dengede kalıyor.","Kefelere yeterli sayıda 1 kg ağırlıklar ekleniyor.","Dengede olması için en az 2 tane 1 kg ağırlık kullanılmış."]},"beginTime":344,"endTime":454,"href":"/video/preview/4915354905333891951?parent-reqid=1769174491020420-11708332147746153643-balancer-l7leveler-kubr-yp-klg-160-BAL&text=15problemzzzz&t=344&ask_summarization=1"},{"index":5,"title":"Şekil Problemi Çözümü","list":{"type":"unordered","items":["Beş kare eşittir üç daire artı bir üçgen.","Bir üçgen artı bir kare eşittir bir daireye eşit.","Kare 2 üçgen, daire 3 üçgen olarak bulunuyor.","Terazinin dengede olması için 4 tane üçgen eklenmesi gerekiyor."]},"beginTime":454,"endTime":667,"href":"/video/preview/4915354905333891951?parent-reqid=1769174491020420-11708332147746153643-balancer-l7leveler-kubr-yp-klg-160-BAL&text=15problemzzzz&t=454&ask_summarization=1"}],"linkTemplate":"/video/preview/4915354905333891951?parent-reqid=1769174491020420-11708332147746153643-balancer-l7leveler-kubr-yp-klg-160-BAL&text=15problemzzzz&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"Problemlerin ritmi sayı ve genel yetenek problemleri 15. soru tipi(ilgili videolar 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Öğretmen, Mito ve Semih adında öğrencilerle etkileşim halindedir.","Videoda hız problemleri konusu detaylı şekilde ele alınmaktadır. İlk olarak iki araç arasındaki durumlar ve \"v1 × t1 = v2 × t2\" formülü anlatılmakta, ardından ortalama hız kavramı ve gidiş-dönüş durumlarında hesaplama yöntemleri açıklanmaktadır. Öğretmen, teorik bilgileri örnek sorular üzerinden uygulamalı olarak göstermektedir.","Video, hız problemlerinde iki püf noktayı vurgulamaktadır: yollar eşitse veya zamanlar eşitse. Ayrıca içler dışlar çarpımı yöntemi, \"çarp-topla\" yöntemi ve farklı hızlarda farklı yolları alan durumlarda toplam yol bölü toplam zaman formülü gibi çözüm teknikleri de detaylı olarak anlatılmaktadır. Video, bir sonraki videoda dairesel hareket, tren ve akıntı sorularının çözüleceği bilgisiyle sonlanmaktadır."]},"endTime":1493,"title":"Hız Problemleri Eğitim Videosu","beginTime":0}],"fullResult":[{"index":0,"title":"Hız Problemlerinde Püf Noktaları","list":{"type":"unordered","items":["Hız problemlerinde iki araç birbirine sıkıntılı durumlar yaratabilir.","Yollar eşit ise veya zamanlar eşit ise, hızlar eşit olamaz.","Yollar eşitse, birinci aracın hızı ile zamanının çarpımı ikinci aracın hızı ile zamanının çarpımına eşittir (v₁t₁ = v₂t₂)."]},"beginTime":9,"endTime":88,"href":"/video/preview/1750106636996347072?parent-reqid=1769174491020420-11708332147746153643-balancer-l7leveler-kubr-yp-klg-160-BAL&text=15problemzzzz&t=9&ask_summarization=1"},{"index":1,"title":"Zamanlar Eşit Durumunda Hız Problemi","list":{"type":"unordered","items":["Zamanlar eşitse, birinci aracın yolu ile ikinci aracın yolunun oranı hızlarının oranına eşittir (x₁/x₂ = v₁/v₂).","Hız problemlerinde iki sıkıntılı durum vardır: yollar eşittir veya zamanlar eşittir.","Aynı zamanda yollar ve zamanlar eşitse, yolların oranı hızların oranına eşittir."]},"beginTime":88,"endTime":165,"href":"/video/preview/1750106636996347072?parent-reqid=1769174491020420-11708332147746153643-balancer-l7leveler-kubr-yp-klg-160-BAL&text=15problemzzzz&t=88&ask_summarization=1"},{"index":2,"title":"Örnek Soru Çözümü","list":{"type":"unordered","items":["Bir araç A ve B kentleri arasındaki yolu v hızıyla 8 saatte alıyor, hızını 20 km arttırırsa 6 saatte alıyor.","Yollar eşit olduğu için v₁t₁ = v₂t₂ denklemi kurulur.","Denklem çözülür ve A ile B arası 480 kilometre olarak bulunur."]},"beginTime":165,"endTime":295,"href":"/video/preview/1750106636996347072?parent-reqid=1769174491020420-11708332147746153643-balancer-l7leveler-kubr-yp-klg-160-BAL&text=15problemzzzz&t=165&ask_summarization=1"},{"index":3,"title":"İkinci Örnek Soru Çözümü","list":{"type":"unordered","items":["Saatteki hızları 60 km ve 90 km olan iki araç A kentinden B kentine aynı anda harekete başlıyor, hızlı giden araç 3 saat önce B'ye varıyor.","Yollar eşit olduğu için v₁t₁ = v₂(t+3) denklemi kurulur.","Denklem çözülür ve A ile B arası 540 kilometre olarak bulunur."]},"beginTime":295,"endTime":457,"href":"/video/preview/1750106636996347072?parent-reqid=1769174491020420-11708332147746153643-balancer-l7leveler-kubr-yp-klg-160-BAL&text=15problemzzzz&t=295&ask_summarization=1"},{"index":4,"title":"Dikdörtgen Şeklindeki Hareket Problemi","list":{"type":"unordered","items":["Bir dikdörtgen şeklindeki soruda, D noktasından aşağı doğru 2v hızla ve sağa doğru 3v hızla hareket eden iki kişi, aynı anda harekete başlayıp K noktasında karşılaşıyorlar.","AB=4BC olduğundan, BC'ye x dersek AB=4x olur ve hızlı olanın aldığı yol 5x+y, yavaş olanın aldığı yol x+4x-y olur.","Zamanların eşit olduğu için yolların oranı hızların oranına eşittir ve içler dışlar çarpımı yapılarak x=y bulunur, böylece KB/KD oranı 1/3 olarak hesaplanır."]},"beginTime":458,"endTime":720,"href":"/video/preview/1750106636996347072?parent-reqid=1769174491020420-11708332147746153643-balancer-l7leveler-kubr-yp-klg-160-BAL&text=15problemzzzz&t=458&ask_summarization=1"},{"index":5,"title":"İki Araç Hareket Problemi","list":{"type":"unordered","items":["A ve B'den aynı anda hareket eden iki araç birbirine doğru gittiğinde C'de karşılaşıyor, bu durumda zamanlar eşit olur.","Hızların oranı yolların oranına eşittir ve 90/120=3/4 olduğundan, hızlı olanın hızı 3v, yavaş olanın hızı 4v olarak belirlenir.","Aynı yöne gittiklerinde D'de buluşuyorlar, bu durumda da zamanlar eşit olur ve içler dışlar çarpımı yapılarak x=630 km olarak bulunur."]},"beginTime":720,"endTime":988,"href":"/video/preview/1750106636996347072?parent-reqid=1769174491020420-11708332147746153643-balancer-l7leveler-kubr-yp-klg-160-BAL&text=15problemzzzz&t=720&ask_summarization=1"},{"index":6,"title":"Ortalama Hız Kavramı","list":{"type":"unordered","items":["Ortalama hız, toplam yol bölü toplam zamandır.","Matematik sınavından alınan notların toplamının sınav sayısına bölünmesi gibi, ortalama hız da toplam yolun toplam zamana bölünmesiyle bulunur.","Bir araç v₁ hızıyla gidip v₂ hızıyla dönerse, ortalama hızı (2×v₁×v₂) / (v₁+v₂) formülüyle hesaplanır."]},"beginTime":994,"endTime":1109,"href":"/video/preview/1750106636996347072?parent-reqid=1769174491020420-11708332147746153643-balancer-l7leveler-kubr-yp-klg-160-BAL&text=15problemzzzz&t=994&ask_summarization=1"},{"index":7,"title":"Ortalama Hız Örnekleri","list":{"type":"unordered","items":["Bir araç AB arasını 40 km/saat hızla gidip 60 km/saat hızla dönerse, ortalama hızı (2×40×60) / (40+60) = 48 km/saat olur.","Bir araç AB yolunun 1/3'ünü 20 km/saat, kalan yolun 1/2'sini 30 km/saat, geri kalan yolu 60 km/saat hızla giderse, ortalama hızı (2×20×30 + 2×30 × 60) / (20 × 20 + 30 × 20 + 30 × 60) = 30 km/saat olur.","Hız problemlerinde zaman, yolun hıza bölümü olarak hesaplanır ve toplam yol bölü toplam 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