Train T leaves station X for station Y at 3 pm. Train S, traveling at three quarters of the speed of T, leaves Y for X at 4 pm. The two trains pass each other at a station Z, where the distance between X and Z is three-fifths of that between X and Y. How many hours does train T take for its journey from X to Y?

### Answer

Train T starts at 3 PM and train S starts at 4 PM.

Let the speed of train T be t.

=> Speed of train S = 0.75t.

When the trains meet, train t would have traveled for one hour more than train S.

Assume that the two trains meet x hours after 3 PM. Trains S would have traveled for x - 1 hours.

Distance traveled by train T = xt

Distance traveled by train S = (x-1)*0.75t = 0.75xt - 0.75t

The train T has traveled three-fifths of the distance. Therefore, train S should have traveled two-fifths the distance between X and Y.

=> (xt) / (0.75xt - 0.75t) = 3/2

2xt = 2.25xt - 2.25t

0.25x = 2.25

x = 9 hours.

So, the train T takes 9 hours to cover three-fifths the distance. Therefore, to cover the entire distance, train T will take 9*(5/3) = 15 hours.

**The correct answer is 15.**