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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.
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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.
Most Upvoted Answer
Train T leaves station X for station Y at 3 pm. Train S, traveling at...
Understanding the Problem
To determine how long Train T takes for its journey from station X to station Y, we start by defining some variables.
- Let the distance between X and Y be denoted as D.
- The distance from X to Z is (3/5)D.
- The distance from Z to Y is (2/5)D.
Train Speeds and Departure Times
- Let speed of Train T be denoted as v.
- Therefore, speed of Train S is (3/4)v.
- Train T departs at 3 pm, while Train S departs at 4 pm.
Time Variables
1. Time taken by Train T to reach Z:
- Train T travels from 3 pm to the time they meet at Z.
- Let the time taken by Train T to reach Z be t hours.
2. Time taken by Train S to reach Z:
- Train S starts at 4 pm, so it travels for (t - 1) hours when they meet at Z.
Setting Up Equations
- The distance traveled by Train T to Z:
- Distance = Speed × Time → (3/5)D = v * t
- The distance traveled by Train S to Z:
- Distance = Speed × Time → (3/5)D = (3/4)v * (t - 1)
Equating Distances
Setting the two distance equations equal:
\[
v * t = (3/4)v * (t - 1)
\]
Canceling v (assuming v ≠ 0) gives:
\[
t = (3/4)(t - 1)
\]
Expanding and solving for t:
\[
4t = 3(t - 1)
\]
\[
4t = 3t - 3
\]
\[
t = 3
\]
Thus, Train T takes 3 hours to reach Z.
Total Journey Time
Since it takes Train T 3 hours to reach Z and they cover the remaining (2/5)D:
Using speed v, the time taken to cover D:
\[
D/v = t + \text{(time to cover remaining distance)}
\]
Total time for Train T:
\[
\text{Total time} = 3 + 12 = 15 \text{ hours}
\]
Thus, Train T takes 15 hours for its journey from X to Y.
To determine how long Train T takes for its journey from station X to station Y, we start by defining some variables.
- Let the distance between X and Y be denoted as D.
- The distance from X to Z is (3/5)D.
- The distance from Z to Y is (2/5)D.
Train Speeds and Departure Times
- Let speed of Train T be denoted as v.
- Therefore, speed of Train S is (3/4)v.
- Train T departs at 3 pm, while Train S departs at 4 pm.
Time Variables
1. Time taken by Train T to reach Z:
- Train T travels from 3 pm to the time they meet at Z.
- Let the time taken by Train T to reach Z be t hours.
2. Time taken by Train S to reach Z:
- Train S starts at 4 pm, so it travels for (t - 1) hours when they meet at Z.
Setting Up Equations
- The distance traveled by Train T to Z:
- Distance = Speed × Time → (3/5)D = v * t
- The distance traveled by Train S to Z:
- Distance = Speed × Time → (3/5)D = (3/4)v * (t - 1)
Equating Distances
Setting the two distance equations equal:
\[
v * t = (3/4)v * (t - 1)
\]
Canceling v (assuming v ≠ 0) gives:
\[
t = (3/4)(t - 1)
\]
Expanding and solving for t:
\[
4t = 3(t - 1)
\]
\[
4t = 3t - 3
\]
\[
t = 3
\]
Thus, Train T takes 3 hours to reach Z.
Total Journey Time
Since it takes Train T 3 hours to reach Z and they cover the remaining (2/5)D:
Using speed v, the time taken to cover D:
\[
D/v = t + \text{(time to cover remaining distance)}
\]
Total time for Train T:
\[
\text{Total time} = 3 + 12 = 15 \text{ hours}
\]
Thus, Train T takes 15 hours for its journey from X to Y.
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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?.
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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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?, a detailed solution 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? has been provided alongside types of 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? theory, EduRev gives you an
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