Two trains leave at the same time, one traveling east and the other traveling west. At the end of 2 hours they are 136 miles apart. If the rate of the train traveling east is 8 miles per hour faster than the rate of the other train, find their rates.
A) 34 miles/hour and 42 miles/hour
B) 24 miles/hour and 32 miles/hour
C) 39 miles/hour and 47 miles/hour
D) 30 miles/hour and 38 miles/hour

Question

Quizplus · Accepted Answer

Let's call the rate of the slower train "x" (in miles/hour). Then the rate of the faster train is x+8 (since it's going 8 miles/hour faster).

In two hours, the slower train travels 2x miles (since distance = rate x time). The faster train travels 2(x+8) miles.

Together, they travel 2x + 2(x+8) = 4x + 16 miles in two hours.

We know this distance is 136 miles. So we can set up an equation:

4x + 16 = 136

Solving for x, we get:

4x = 120

x = 30

So the slower train is traveling at 30 miles/hour, and the faster train is traveling at x+8 = 38 miles/hour.

Therefore, the answer is D.

Two Trains Leave at the Same Time, One Traveling East