Question

A passenger train traveled 180 miles in the same amount of time it took a freight train to travel 120 miles. The rate of the freight train was 15 miles per hour slower than the rate of the passenger train. Find the rate of the passenger train.

Answer 1

The passenger train is moving at 45 miles per hour

Explanation:

Let the amount of time it took the two trains to travel the distance = t.

Since the two trains traveled the distance at the same time,

Rate of the passenger train =
`(180)/(t)`

Rate of the freight train =
`(120)/(t)`

Where t is in hours.

From the problem, we can see that the rate of the freight train was 15 miles per hour slower than the rate of the passenger train. Mathematically, we can represent this as

`(120)/(t)= (180)/(t)-15`

from the above equation, we can now get our value for t as

`(120-180)/(t)=-15\\(-60)/(t)=-15\\t=4 hours`

We have our time of travel for the two trains as 4 hours.

The rate of the passenger train can now be calculated by 180/4 = 45 miles per hour