Find the speed of each train.?

Question

The speed of a passenger train is 6 mph faster than the speed of a freight train. The passenger train travels 310 miles in the same time it takes the freight train to travel 280 miles. Find the speed of each train.

What is the speed of the passenger train? __mph

What is the speed of the freight train? __mph

Answer 1

We know that the passenger train travels 6 miles per hour faster, and in the same length of time travels 30 miles (310 - 280) further.

If the passenger train travels 6 miles further every hour, and 30 miles further in total, then it must have traveled for 30 / 6 = 5 hours:

30 miles / ( 6 miles / hour) = 30 miles * (1 hour / 6 miles) = 5 hours

So in 5 hours the passenger train traveled 310 miles. Therefore it's speed is the following:

310 miles / 5 hours = 62 miles per hour

The freight train traveled for the same length of time, so in 5 hours it traveled 280 miles. Therefore it's speed is the following:

280 miles / 5 hours = 56 miles per hour

As a check of our work, remember the passenger train travels 6 miles per hour faster than the freight train. Our answers back this fact up as 62 mph - 56 mph = 6 mph.

QED