Help with word problem..?

Question

Trains A and B are traveling in the same direction on parallel tracks. Train A is traveling at 100 miles per hour and train B is traveling 110 miles per hour. Train A passes a station at 7:10am. If train B passes the same station at 7:40am, at what time will train B catch up to train A?

Answer 1

To solve this you need to create two simultaneous equations.

Calculate the distance already travelled by Train A

d = st

d = distance

s = speed

t = time

So

d = 100miles/h*h/2

   = 50 miles

This is the initial distance between Train A and B

We know that Train A travels x distance and Train B travels x + 50 distance, and they both travel for the same time t.

Equation 1

A              s = d/t

100miles/h = x/t

B

110miles/h = (50 + x)/t

Make x the subject

A

x = 100t

B

x = 110t - 50

Therefore A = B

110t - 50 = 100t

10t = 50

t = 5

Therefore it takes 5 hours for both trains to meet, which is 12:40pm

And the distance is 500 miles