AMC10 2022 B

AMC10 2022 B · Q4

AMC10 2022 B · Q4. It mainly tests Rates (speed), Arithmetic misc.

A donkey suffers an attack of hiccups and the first hiccup happens at $4:00$ one afternoon. Suppose that the donkey hiccups regularly every $5$ seconds. At what time does the donkey’s $700$th hiccup occur?

一头驴打嗝，第一声嗝发生在下午4:00。假设驴每5秒规律地打一次嗝。驴的第700次嗝发生在几点？

(A) 15 \text{ seconds after } 4:58 15 \text{ seconds after } 4:58

(B) 20 \text{ seconds after } 4:58 20 \text{ seconds after } 4:58

(D) 30 \text{ seconds after } 4:58 30 \text{ seconds after } 4:58

(E) 35 \text{ seconds after } 4:58 35 \text{ seconds after } 4:58

Answer

Correct choice: (A)

正确答案：（A）

Solution

Since the donkey hiccupped the 1st hiccup at $4:00$, it hiccupped for $5 \cdot (700-1) = 3495$ seconds, which is $58$ minutes and $15$ seconds, so the answer is $\boxed{\textbf{(A) }15 \text{ seconds after } 4:58}$.

由于驴在4:00打出第1次嗝，它总共打了$5 \cdot (700-1) = 3495$秒，即58分钟15秒，因此答案是$\boxed{\textbf{(A) }4:58后15 \text{ 秒}}$。

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