This no-calculator prompt is from the Daily Practice app:

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

In 15 seconds at 5 m/sec, Sam will be 75 m ahead when Lisa starts running. Once she starts running, Lisa is going to gain 3 m/sec on Sam. How many seconds will it take to cover that 75 m gap at 3 m/sec?

    \begin{align*}\frac{75\text{ m}}{3\text{ m/sec}}=25\text{ sec}\end{align*}

The trick to this question is recognizing that you’re being asked (at least I think you’re being asked—the wording is not very precise) how many seconds have passed when Lisa catches up to Sam since the race started. You have to include Sam’s 15 second head start. Sam ran for 15 seconds, then both Lisa and Sam ran for 25 seconds, then Lisa caught up to Sam. Total elapsed time: 40 seconds.

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