An express train and a local train both leave Gray's Lake at 3 P.M. and head for Chicago 50 miles away. The express travels twice as fast as the local and arrives 1 hour ahead of the local. Find the speed of each train.
A) Express: $25 \mathrm{mph}$; local: $12.5 \mathrm{mph}$
B) Express: $50 \mathrm{mph}$; local: $25 \mathrm{mph}$
C) Express: $60 \mathrm{mph}$; local: $30 \mathrm{mph}$
D) Cannot be determined without more information

Question

Quizplus · Accepted Answer

The express train travels twice as fast as the local train and arrives 1 hour earlier. If the local train's speed is $x$, then the express train's speed is $2x$. The local train takes $\frac{50}{x}$ hours, and the express train takes $\frac{50}{2x}$ hours. The difference in time is 1 hour: $\frac{50}{x} - \frac{50}{2x} = 1$. Solving this equation gives $x = 25$, so the local train's speed is $25 \mathrm{mph}$ and the express train's speed is $50 \mathrm{mph}$.

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An Express Train and a Local Train Both Leave Gray's $25 \mathrm{mph}$