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Giải bài 52 trang 42 sách bài tập Toán 6 – Cánh Diều Tập 2

Tải về
Bây giờ là 12 giờ. Sau ít nhất bao nhiêu phút nữa thì kim giờ và kim phút vuông góc với nhau?

🧜Tổng hợp đề thi học kì 2 lớp 6 tất cả các môn - Cánh diều

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

Bây giờ là 12 giờ. Sau ít nhất bao nhiêu phút nữa thì kim giờ và kim phút vuông góc với nhau?

Phương pháp giải - Xem chi tiết

Quan sát trên đồng đồ, nếu kim giờ và kim phút cách nhau đúng 15 vạch thì 2 kim vuông góc với nhau. Mỗi giờ, kim giờ đi được 5 vạch, kim phút đi qua 60 vạch. Hay vận tốc của kim phút gấp 12 lần vận tốc của kim giờ.

Lời giải chi tiết

Giả sử sau x phút thì 2 kim vuông góc.Vì: mỗi giờ, kim giờ đi được 5 vạch, kim phút đi qua 60 vạch.Nên: mỗi phút, kim giờ đi được \(\frac{5}{{60}} = \frac{1}{{12}}\)vạch, kim phút đi được 1 vạchTa có: Sau x phút, 2 kim vuông góc hay:\(x.1 - x.\frac{1}{{12}} = 15\)( Vì kim phút chạy nhanh hơn nên quãng đường đi được lớn hơn)\( \Rightarrow x\left( {1 - \frac{1}{{12}}} \right) = 15 \Leftrightarrow x = 15:\left( {1 - \frac{1}{{12}}} \right) = \frac{{180}}{{11}} = 16\frac{4}{{11}}\) (phút)Vậy sau \(16\frac{4}{{11}}\) phút nữa thì hai kim vuông góc với nhau.
Tải về

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