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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?
(2018)
  • a)
    15
  • b)
    16
  • c)
    13
  • d)
    17
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Train T leaves station X for station Y at 3 pm. Train S, traveling at ...
Let the time taken by S to reach Z be t hours.
Let the speed of T be St. Distance between X and Z is 3/5 of the distance between X and Y.
XZ : ZY = 3 : 2

t = 8
S takes 8 hours to cover YZ.
T would take 8 × (3/4) i.e. 6 hours to cover ZY.
T would take t + 1 i.e. 9 hours to cover XZ.
T would take 15 hours to reach Y.
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Most Upvoted Answer
Train T leaves station X for station Y at 3 pm. Train S, traveling at ...
To solve this question, let's break down the information given step by step:

1. Train T leaves station X for station Y at 3 pm.
2. Train S, traveling at three-quarters of the speed of T, leaves Y for X at 4 pm.
3. The two trains pass each other at a station Z.
4. The distance between X and Z is three-fifths of the distance between X and Y.

Let's find the time it takes for the two trains to meet at station Z.

Step 1: Calculate the time it takes for Train T to reach Z
- Let's assume that the distance between X and Z is 3x.
- Since Train T leaves at 3 pm, it travels for 1 hour to reach Z.
- Let the speed of Train T be v.
- Therefore, the equation for Train T is: v * 1 = 3x

Step 2: Calculate the time it takes for Train S to reach Z
- Since Train S leaves at 4 pm, it travels for t hours to reach Z.
- The speed of Train S is three-quarters of the speed of Train T, so its speed is (3/4)v.
- Therefore, the equation for Train S is: (3/4)v * t = 3x

Step 3: Equate the distances covered by Train T and Train S
- Since the distance covered by Train T is the same as that covered by Train S, we can equate the equations from Steps 1 and 2:
v * 1 = (3/4)v * t

Step 4: Solve for t
- Dividing both sides of the equation by v, we get:
1 = (3/4)t
- Multiplying both sides by 4/3, we get:
4/3 = t
- Therefore, t = 4/3.

Step 5: Calculate the total time taken by Train T from X to Y
- Since Train T reaches Z in 1 hour and Train S takes t = 4/3 hours to reach Z, the total time taken by Train T from X to Y is 1 + 4/3 = 7/3 hours.

Converting the time to minutes:
7/3 hours = 140/60 minutes = 2 hours and 20 minutes.

Therefore, Train T takes 2 hours and 20 minutes for its journey from X to Y.

The correct answer is option A) 15.
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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?(2018)a)15b)16c)13d)17Correct answer is option 'A'. Can you explain this answer?
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