This question is a little tougher than it looks. From the average solve times, it shows that it takes quite sometime to complete. Here is how it is solved --
Let's assume the following :
Distance between X and Y = D --> 1
R(T) --> Rate of Train T --> 2
R(S) --> Rate of Train S -> 3
Given -->
R(S) = 3/4 [R(T)] --> 4
Distance from Station X to Z = 3/5(D) --> 5
Distance from Station Y to Z = 2/5(D) --> 6
Train T leaves Station X at 3:00 PM --> 7
Train S leaves Station Y at 4:00 PM --> 8
From the above given points (7 & 8), we can conclude that Train T travels for 1 hour while Train S is stationary
So, using the Distance = Rate x Time formula, we can conclude that Train T travels a distance (say a). This can be mentioned in the formula as --> a = R(T) --> 9
Using points 5 and 9, we can conclude that after Train T travels for an hour (Lets name this position an arbitrary position O), the remaining distance to Station Z = 3/5(D) - a = 3/5(D) - R(T) --> 10
Now Train T has to travel to Station Z from O and Train S has to travel to Station Z from Y (Two Objects travelling towards each other)
When two objects travel towards each other, you can sum up their rates, the distance they travel becomes the total distance and time traveled by both the objects remains the same. So we have --
R(T) + R(S) = [3/5(D) - R(T) + 2/5(D)] / T(Time to reach Station Z) --> 11
T(Time to reach station Z) = Time taken by Train T from O to Z (OR) Time taken by Train S from Y to Z [T(S)] --> 12
From the given rates, we can write the following for equation 12--> T(S) = [2/5(D)] /[3/4(R(T)] = 8D/[15(R(T))] --> 13
We can substitute equations 4 & 13 in equation 11. After solving we end up with D = 15R(T) --> It takes Train T 15 hours to travel from Station X to Station Y @ rate R(T)
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Siddharth Ramachandran
B School Aspirant, 2021 Intake