How do you solve this train problem? It has no distance or speed. It only gives you the time it takes to finish the distance for both trains.

Question

Train X takes 10 hours to travel from station A to station B, while train Y takes 15 hours to travel from station B to station A. If train X and Y starts at same time from stations A and B respectively, trains will cross each other after(How many) hours.

Answer 1

You can solve this without knowing the distance because it will cancel out. Suppose the distance between A and B is d.

d/10 = speed of train x

d/15 = speed of train y

Now suppose they meet at time t going in opposite directions. Suppose train x travels to the right and train y travels to the left. The two trains must arrive at the same point at time t. Train x arrives at position (d/10)t while train y arrives at position d - (d/15)t. These two positions must be the same, so

(d/10)t = d - (d/15)t ⇒

t/10 = 1 - t/15

Solve for t.

t = 10 - (2/3)t

(5/3)t = 10

t = 10(3/5) = 6

They meet in 6 hours.