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Question

A freight train and an express train leave towns 390390 miles apart at the same time, traveling toward one another. The freight train travels 30 mph30 \text{ mph} slower than the express train. They pass one another 33 hours later. What are their speeds?

Solution

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Answered 2 years ago
Answered 2 years ago
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Let s1s_1 be the speed of freight train, and let s2s_2 be the speed of express train.

We know that the speed ss is:

s=dt,  (1)\boxed{s=\dfrac{d}{t},~~(1)}

where dd is distance and tt is time.

From (1) we get d=std=st. So the freight train in 3 hours passed d1=3s1d_1=3s_1 and express train passed d2=3s2d_2=3s_2

  • both trains travel 3 hours and together they covered 390 miles, so we get

d1+d2=3903s1+3s2=390d_1+d_2=390\Rightarrow 3s_1+3s_2=390

  • we also know that freight train travels 30 mph slower than express train, so we get:

s1=s230s_1=s_2-30

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