Two trains are in constant motion between New York and Philadelphia, which are 150 miles apart. Train A leaves New York while Train B departs from Philadelphia at the same time. The speeds of Train A and Train B are 50 miles per hour and 100 miles per hour, respectively. If we disregard any turnaround times at the stations, what is the distance between the locations where the trains first and second meet?

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25 miles

50 miles

Correct

75 miles

150 miles

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Official Explanation

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The time taken for both trains to meet for the first time is calculated as

\frac{150}{50+100}

=1.5 ext{ hours}. The time taken for both trains to meet for the second time is

\frac{300}{50+100}

=3 ext{ hours}. The distance of…

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What this question tests

Your application of distance = rate × time to trains, boats, and commuters, including relative speed.

Mixing units (miles per hour vs. minutes) or averaging speeds — average speed is total distance over total time.