Two trains leave the station at the same time, one heading west(100mph), the other heading east90mph. how long will it take the two trains to be 456 mile apart?

Question

Two trains leave the station at the same time, one heading west, the other heading east. The westbound train travels at a speed of 100 mph. The east bound train travels at a speed of 90 mph. how long will it take the two trains to be 456 mile apart?

Answer 1

The trains are receding from each other at a rate of 100mph + 90mph = 190mph. They have to cover 456 miles. It helps to reframe the question using more familiar numbers. If you're driving at 50mph and want to travel 100 miles, how long will it take you? Two hours. 100 miles / 50 mph = 2 hours. And the same technique will work for our trains. 456 miles / 190 mph = 2.4 hours. 

 

The trickiest part of solving the question, perhaps, is to recognize that you need to add the trains' velocities together. 

Answer 2

Distance = Rate x Time

456 = 100 + 90 + Time or

Time = 456/190 = 2.4 hours

Answer 3

distance=rate*time

456=100*t+90t

456=190*t

t=456/190

t=2.4 hours