Question

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 1

Calculation:

Let distance between X and Y be a km.

⇒ XZ = 3/5 × XY

⇒ XZ = 3a/5

⇒ ZY = a - 3a/5 = 2a/5

Let speed of train T be v kmph.

Speed of train S = v × 3/4 kmph

⇒ (3a/5v) - 1 = 8a/15v

Let a/v = m.

⇒ 3m/5 - 1 = 8m/15

⇒ m = 15

⇒ a/v = 15

∴ Time taken by train T to complete journey of X to Y = 15 hours