distance rate time question

Question

Two trains leave the station at the same time, one heading east and the other west. The eastbound train travels at
55
miles per hour. The westbound train travels at
75
miles per hour. How long will it take for the two trains to be
208
miles apart?

Answer 1

Remember that distance = (rate)(time). We'll write two equations, one for the eastbound train and one for the westbound train.

 

 

 

EASTBOUND TRAIN:

 

We don't know how far the train travels, so call its distance d. The train travels at a rate of 55 mph. We don't know how long the train travels, so call its time t.

 

d = 55t

 

 

 

WESTBOUND TRAIN:

 

We don't know how far the train travels, but we do know that together the trains must travel 208 miles. So, call its distance 208 - d. The train travels at a rate of 75 mph. We don't know how long the train travels, but we do know it travels for the same amount of time as the other train, so call its time t.

 

208 - d = 75t

 

 

 

Now you've got a system of two equations:

 

d = 55t

208 - d = 75t

 

Plug the first equation into the second equation and solve for t:

 

208 - d = 75t

208 - 55t = 75t

208 = 130t

1.6 = t

 

The trains travel for t = 1.6 hours, or 1 hour and 0.6(60) = 36 minutes.