A freight train travels 90 miles in the same time that a pas

A freight train travels 90 miles in the same time that a passenger train travels 150 miles. If the passenger train goes 30 miles per hour faster than the freight train, what is the rate of each of them?

Solution

let us the speed of freight train=x

the speed of passenger train =y

A freight train travels 90 miles in the same time that a passenger train travels 150 miles.

So, 90/x= 150/y or, x= 90y/150= 3y/5

and the passenger train goes 30 miles per hour faster than the freight train

y=x+30

plug x=3y/5

y=3y/5 +30

y-3y/5=30

2y/5 = 30

2y=30*5=150

y=150/2=75 miles/hour

Since, y=x+30

75=x+30

x=75-30=45