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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-๏ฌfths 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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Explanatory Answer

Method of solving this CAT Question from Speed Time Distance
Speed Time Distance - Finding the time taken

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{3๐‘‘}{4๐‘ฃ}) hrs ---(1)
Time (S to reach Z) = \\frac{2๐‘‘}{3๐‘ฃ}) 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{3๐‘‘}{4๐‘ฃ}) - 1 = \\frac{2๐‘‘}{3๐‘ฃ})

Let \\frac{d}{v}) = k
\\frac{3}{4})k - \\frac{2}{3})k = 1
k = 12
So, \\frac{5๐‘‘}{4๐‘ฃ}) = \\frac{5 ร— 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-๏ฌfths of that between X and Y. How many hours does train T take for its journey from X to Y? [TITA]"

Hence, the answer is 15 hours

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