每日一题

Mathematics

Lisa gives her little brother Sam a 15-second(sec) head start in a 300-meter(m) race. During the race, Sam runs at an average speed of 5 m/sec and Lisa runs at an average speed of 8 m/sec, not including the head start. Which of the following best approximates the number of seconds that had passed when Lisa caught up to Sam?

A.5
B.25
C.40
D.55

答案和解析

答案：B

解析：

Choice B is correct. Let t represent the time, in seconds, that Sam spends running, let d represent the distance run, and let r represent the rate at which Sam is moving.

Then, since d=rt, 5t represents the total distance, in meters, Sam runs in t seconds.

Since Lisa gives her little brother a 15-second head start, it follows that she runs for t-15 seconds at a rate of 8 m/sec.

So, 8(t-15) represents the total distance, in meters, Lisa runs in(t-15) seconds.

If Lisa catches Sam, they would have covered the same distance. Therefore, we can set up the following equation and solve for t:

8(t-15)=5t

8t-120=5t

3t=120

t=40

Since t represent the time, in seconds, that Sam spends running, this shows that Sam will run for 40 seconds before his sister catches him.

Since Lisa runs for t-15 seconds, it follows that she runs for 25 seconds before catching up with Sam.