Question

A passenger train traveled 100 miles in the same amount of time it took a freight train to travel 80 miles. The rate of the freight train was 5 miles per hour slower than the rate of the passenger train. Find the rate of the passenger train.

Answer 1

The passenger train traveled at a speed of 25 miles/hour

Explanation:

In this question, we are asked to calculate the rate at which a particular passenger train is traveling.

We use the information in the question to answer as follows;

Firstly, we identify that they traveled at the same time but their distances are different. This means that their speed must be different also.

Mathematically, we know that time can be calculated as distance/ time.

Let us say the speed at which the passenger train traveled is x miles per hour. This means that the speed of the freight train which was 5 miles per hour slower would be (x-5) miles per hour.

We know their times are equal;

Hence;

100/x = 80/(x-5)

We cross multiply

100(x-5) = 80x

100x -500 = 80x

100x-80x = 500

20x = 500

x = 500/20

x = 25 miles per hour