Two Trains Journey Time

CAT 2019 Slot 1 · QA · Easy · Speed, Time and Distance

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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

15

Explanation

Let total distance XY=DXY = D. Distance XZ=0.6DXZ = 0.6D, ZY=0.4DZY = 0.4D. Let speed of T = vv, speed of S = 0.75v0.75v. T starts at 3 pm, travels till meeting time tt. In first 1 hour (3 pm to 4 pm), T travels 1×v=v1 \times v = v. Remaining distance for T to reach Z = 0.6D−v0.6D - v. S starts at 4 pm and covers 0.4D0.4D to reach Z. Time from 4 pm to meeting = 0.4D0.75v=0.6D−vv\frac{0.4D}{0.75v} = \frac{0.6D - v}{v}. 0.4D0.75=0.6D−v⇒815D=0.6D−v⇒v=0.6D−0.5333D=115D\frac{0.4D}{0.75} = 0.6D - v \Rightarrow \frac{8}{15}D = 0.6D - v \Rightarrow v = 0.6D - 0.5333D = \frac{1}{15}D. So speed v=D15v = \frac{D}{15}, meaning T takes Dv=15\frac{D}{v} = 15 hours.

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