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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?
Correct answer is '15'. Can you explain this answer?
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Train T leaves station X for station Y at 3 pm. Train S, traveling at ...
Train T starts at 3 PM and train S starts at 4 PM.
Let the speed of train T be t.
=> Speed of train S = 0.75t.
When the trains meet, train t would have traveled for one more hour than train S.
Let us assume that the 2 trains meet x hours after 3 PM. Trains S would have traveled for x-1 hours.
Distance traveled by train T = xt Distance traveled by train S = (x-1)*0.75t = 0.75xt-0.75t We know that train T has traveled three fifths of the distance. Therefore, train S should have traveled two-fifths the distance between the 2 cities.
=> (xt)/(0.75xt-0.75t) = 3/2
2xt = 2.25xt-2.25t
0.25x = 2.25
x = 9 hours.
Train T takes 9 hours to cover three-fifths the distance. Therefore, to cover the entire distance, train T will take 9*(5/3) = 15 hours.
Therefore, 15 is the correct answer.
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Train T leaves station X for station Y at 3 pm. Train S, traveling at ...
Analysis:
To solve this problem, we need to find the time taken by train T for its journey from X to Y. We are given the following information:
- 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.

Step 1: Find the time taken by Train S to reach station Z
Let's assume the distance between X and Y as D. According to the given information, the distance between X and Z is three-fifths of D. Therefore, the distance between Z and Y is D - (3/5)D = (2/5)D.

Since Train S leaves Y for X at 4 pm, it travels for 1 hour to reach Z. Let's assume the speed of Train S as Ss and the speed of Train T as St. We are given that Ss = (3/4)St.

Using the formula: Speed = Distance/Time, we can write the equation for Train S as:
Ss = (2/5)D / 1 hour

Simplifying the equation, we get:
(3/4)St = (2/5)D
St = (8/15)D

Step 2: Find the time taken by Train T to reach station Z
Since Train T leaves station X at 3 pm and the two trains pass each other at Z, Train T travels for (4 pm - 3 pm) = 1 hour to reach Z. Let's assume the time taken by Train T to reach Z as Tt.

Using the formula: Speed = Distance/Time, we can write the equation for Train T as:
St = (3/5)D / Tt

Simplifying the equation, we get:
(8/15)D = (3/5)D / Tt
Tt = (3/5) / (8/15)
Tt = (3/5) * (15/8)
Tt = 9/8

Step 3: Find the time taken by Train T to reach station Y
Since Train T travels for Tt hours to reach Z, it will travel for the remaining time to reach Y. The total time taken by Train T for its journey from X to Y can be calculated as:
Total time = Time taken to reach Z + Time taken to reach Y

Total time = 1 hour + Tt
Total time = 1 hour + 9/8
Total time = 17/8

Step 4: Convert the total time into hours
Since the total time is given as 17/8, we need to convert it into hours. Dividing 17 by 8, we get:
Total time = 2 hours + 1/8

Therefore, the total time taken by Train T for its journey from X to Y is 2 hours and 1/8 hour, which is equivalent to 2 hours and 7.5 minutes.

Step 5: Convert the time into minutes
Since the total time is given as
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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?Correct answer is '15'. Can you explain this answer?
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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?Correct answer is '15'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about 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?Correct answer is '15'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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?Correct answer is '15'. Can you explain this answer?.
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