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Giải Bài 2.48 trang 55 SGK Toán 6 Kết nối tri thức với cuộc sống tập 1

Hai vận động viên chạy xung quanh một sân vận động. Hai vận động viên xuất phát tại cùng một thời điểm, cùng vị trí và chạy cùng chiều. Vận động viên thứ nhất chạy một vòng sân hết 360 giây, vận động viên thứ hai chạy một vòng sân mất 420 giây. Hỏi sau bao nhiêu phút họ lại gặp nhau, biết tốc độ di chuyển của họ không đổi?

♓Tổng hợp đề thi học kì 2 lớp 6 tất cả các môn - Kết nối tri thức

Toán - Văn - Anh - Khoa học tự nhiên...
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Đề bài

Hai vận động viên chạy xung quanh một sân vận động. Hai vận động viên xuất phát tại cùng một thời điểm, cùng vị trí và chạy cùng chiều. Vận động viên thứ nhất chạy một vòng sân hết 360 giây, vận động viên thứ hai chạy một vòng sân mất 420 giây. Hỏi sau bao nhiêu phút họ lại gặp nhau, biết tốc độ di chuyển của họ không đổi?

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

*Các bước tìm BCNN: - Phân tích mỗi số ra thừa số nguyên tố, - Chọn ra các thừa số nguyên tố chung và riêng; - Lập tích các thừa số đã chọn, mỗi thừa số lấy với số mũ lớn nhất. Tích đó là BCNN cần tìm.

Lời giải chi tiết

Đổi 360 giây = 6 phút, 420 giây = 7 phútGiả sử họ lại gặp nhau sau x (phút)( x > 0)Vận động viên thứ nhất chạy một vòng sân hết 6 phút nên x là bội của 6.Vận động viên thứ hai chạy một vòng sân hết 7 phút nên x là bội của 7.

Nên x ∈ BC(6, 7).

Mà x ít nhất nên x = BCNN(6, 7).

Ta có: 6 = 2.3; 7 = 7

x = BCNN(6, 7) = 2.3.7 = 42

Vậy sau 42 phút họ lại gặp nhau.

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