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Question 23 :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? [TITA]

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From question, XZ = 3d, YZ = 2d

As their speeds are in ratio 4:3

Let their speeds be 4V and 3V

Time (T to reach Z) = \\frac{3𝑑}{4𝑣}) hrs ---(1)

Time (S to reach Z) = \\frac{2𝑑}{3𝑣}) hrs ---(2)

We need to find the time taken for T To travel from X to Y

Time = \\frac{5d}{4v})

Train S started one hour late than Train T

=> \\frac{3𝑑}{4𝑣}) - 1 = \\frac{2𝑑}{3𝑣})

Let \\frac{d}{v}) = k

\\frac{3}{4})k - \\frac{2}{3})k = 1

k = 12

So, \\frac{5𝑑}{4𝑣}) = \\frac{5 × 12}{4}) = **15 hours**

The question is **"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? [TITA]" **

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