AMC8 2003

AMC8 2003 · Q20

AMC8 2003 · Q20. It mainly tests Fractions, Angle chasing.

What is the measure of the acute angle formed by the hands of a clock at 4:20 a.m.?

4:20 a.m. 时钟指针形成的锐角是多少度？

(A) 0° 0°

(B) 5° 5°

(D) 10° 10°

(E) 12° 12°

Answer

Correct choice: (D)

正确答案：（D）

Solution

At 4:00 a.m., the minute hand is at 12 and the hour hand is at 4. By 4:20 a.m., the minute hand has moved $\frac{1}{3}$ of way around the clock to 4, and the hour hand has moved $\frac{1}{12} \times \frac{1}{3} = \frac{1}{36}$ of the way around the clock from 4. Therefore, the angle formed by the hands at 4:20 a.m. is $\frac{1}{36} \cdot 360^\circ = 10^\circ$.

在 4:00 a.m. 时，分针在 12 位置，时针在 4 位置。到 4:20 a.m. 时，分针已经转动了绕钟 $\frac{1}{3}$ 的路程到 4 位置，时针从 4 位置转动了 $\frac{1}{12} \times \frac{1}{3} = \frac{1}{36}$ 的绕钟距离。因此，4:20 a.m. 时钟指针形成的角是 $\frac{1}{36} \cdot 360^\circ = 10^\circ$。

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