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Two athletes run around a circular track in opposite direction and their speeds are in the ratio 2 : 3. If they start from the same point and the slower one takes 15 minutes to complete one round then find the time, in minutes, after which they meet each other for the first time.
Correct answer is '6'. Can you explain this answer?
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Verified Answer
Two athletes run around a circular track in opposite direction and the...
Let the speed of two athletes be 2x and 3x respectively.
The slower one takes 15 minutes to complete one full round.
The length of the track = 15 * 2x = 30x
Since, they travel in opposite directions from the same point,
The time taken = (circumference of the track) / (sum of the speeds) = 30x1 (2x + 3x) = 6 minutes
Answer: 6
The slower one takes 15 minutes to complete one full round.
The length of the track = 15 * 2x = 30x
Since, they travel in opposite directions from the same point,
The time taken = (circumference of the track) / (sum of the speeds) = 30x1 (2x + 3x) = 6 minutes
Answer: 6
Most Upvoted Answer
Two athletes run around a circular track in opposite direction and the...
Given:
To find:
The time after which they meet each other for the first time.
Solution:
Let's assume the distance of the circular track is D.
Let the speeds of the slower and faster athletes be 2x and 3x respectively.
Step 1: Find the time taken by the faster athlete to complete one round.
The ratio of speeds of the two athletes is 2:3.
Let's assume the distance of the circular track is D.
Then the faster athlete will cover the distance D in less time than the slower athlete.
Let's assume the faster athlete takes T minutes to complete one round.
Then, using the formula Speed = Distance/Time, we get:
- Speed of slower athlete = D/15
- Speed of faster athlete = D/T
As per the given ratio, we have:
- Speed of slower athlete: Speed of faster athlete = 2:3
Therefore,
- (D/15)/(D/T) = 2/3
- T/15 = 3/2
- T = 22.5 minutes
So, the faster athlete takes 22.5 minutes to complete one round.
Step 2: Find the time taken by the two athletes to meet each other for the first time.
When the two athletes start from the same point and run in opposite directions, they will meet each other after covering a distance equal to the sum of their distances.
Let's assume that they meet after t minutes.
In t minutes, the slower athlete will cover a distance of (2x) * (t/15) = (2tx)/15
In t minutes, the faster athlete will cover a distance of (3x) * (t/22.5) = (2tx)/15
So, the distance covered by both athletes will be equal when they meet each other for the first time.
Therefore,
- (2tx)/15 = (3tx)/22.5
- t = 6 minutes
Therefore, the two athletes will meet each other for the first time after 6 minutes.
Final Answer: 6
- The ratio of speeds of two athletes is 2:3.
- The slower athlete takes 15 minutes to complete one round.
To find:
The time after which they meet each other for the first time.
Solution:
Let's assume the distance of the circular track is D.
Let the speeds of the slower and faster athletes be 2x and 3x respectively.
Step 1: Find the time taken by the faster athlete to complete one round.
The ratio of speeds of the two athletes is 2:3.
Let's assume the distance of the circular track is D.
Then the faster athlete will cover the distance D in less time than the slower athlete.
Let's assume the faster athlete takes T minutes to complete one round.
Then, using the formula Speed = Distance/Time, we get:
- Speed of slower athlete = D/15
- Speed of faster athlete = D/T
As per the given ratio, we have:
- Speed of slower athlete: Speed of faster athlete = 2:3
Therefore,
- (D/15)/(D/T) = 2/3
- T/15 = 3/2
- T = 22.5 minutes
So, the faster athlete takes 22.5 minutes to complete one round.
Step 2: Find the time taken by the two athletes to meet each other for the first time.
When the two athletes start from the same point and run in opposite directions, they will meet each other after covering a distance equal to the sum of their distances.
Let's assume that they meet after t minutes.
In t minutes, the slower athlete will cover a distance of (2x) * (t/15) = (2tx)/15
In t minutes, the faster athlete will cover a distance of (3x) * (t/22.5) = (2tx)/15
So, the distance covered by both athletes will be equal when they meet each other for the first time.
Therefore,
- (2tx)/15 = (3tx)/22.5
- t = 6 minutes
Therefore, the two athletes will meet each other for the first time after 6 minutes.
Final Answer: 6
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Community Answer
Two athletes run around a circular track in opposite direction and the...
2x-->1/15
5x-->1/6
thus 6 mins
5x-->1/6
thus 6 mins
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Two athletes run around a circular track in opposite direction and their speeds are in the ratio 2 : 3. If they start from the same point and the slower one takes 15 minutes to complete one round then find the time, in minutes, after which they meet each other for the first time.Correct answer is '6'. Can you explain this answer?
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Two athletes run around a circular track in opposite direction and their speeds are in the ratio 2 : 3. If they start from the same point and the slower one takes 15 minutes to complete one round then find the time, in minutes, after which they meet each other for the first time.Correct answer is '6'. 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 Two athletes run around a circular track in opposite direction and their speeds are in the ratio 2 : 3. If they start from the same point and the slower one takes 15 minutes to complete one round then find the time, in minutes, after which they meet each other for the first time.Correct answer is '6'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two athletes run around a circular track in opposite direction and their speeds are in the ratio 2 : 3. If they start from the same point and the slower one takes 15 minutes to complete one round then find the time, in minutes, after which they meet each other for the first time.Correct answer is '6'. Can you explain this answer?.
Two athletes run around a circular track in opposite direction and their speeds are in the ratio 2 : 3. If they start from the same point and the slower one takes 15 minutes to complete one round then find the time, in minutes, after which they meet each other for the first time.Correct answer is '6'. 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 Two athletes run around a circular track in opposite direction and their speeds are in the ratio 2 : 3. If they start from the same point and the slower one takes 15 minutes to complete one round then find the time, in minutes, after which they meet each other for the first time.Correct answer is '6'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two athletes run around a circular track in opposite direction and their speeds are in the ratio 2 : 3. If they start from the same point and the slower one takes 15 minutes to complete one round then find the time, in minutes, after which they meet each other for the first time.Correct answer is '6'. Can you explain this answer?.
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Two athletes run around a circular track in opposite direction and their speeds are in the ratio 2 : 3. If they start from the same point and the slower one takes 15 minutes to complete one round then find the time, in minutes, after which they meet each other for the first time.Correct answer is '6'. Can you explain this answer?, a detailed solution for Two athletes run around a circular track in opposite direction and their speeds are in the ratio 2 : 3. If they start from the same point and the slower one takes 15 minutes to complete one round then find the time, in minutes, after which they meet each other for the first time.Correct answer is '6'. Can you explain this answer? has been provided alongside types of Two athletes run around a circular track in opposite direction and their speeds are in the ratio 2 : 3. If they start from the same point and the slower one takes 15 minutes to complete one round then find the time, in minutes, after which they meet each other for the first time.Correct answer is '6'. Can you explain this answer? theory, EduRev gives you an
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