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Starting from the same point at the same time, A and B run on a 3600 m circular track with speeds of 4 m/s and 6 m/s, clockwise. After A completes the first round on the track, she reverses direction and runs anticlockwise. After how many seconds of starting the run would they cross for the first time?
- a)1200
- b)1620
- c)1080
- d)1020
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
Starting from the same point at the same time, A and B run on a 3600 m...
To find out when A and B will cross each other for the first time, we can calculate the time it takes for each person to complete one full round and find the point of intersection.
Let's assume the circumference of the circular track is C = 3600 m.
Calculating the time taken by A to complete one full round:
Speed of A = 4 m/s
Distance covered by A in one round = C = 3600 m
Time taken by A to complete one round = Distance/Speed = 3600/4 = 900 seconds
Calculating the time taken by B to complete one full round:
Speed of B = 6 m/s
Distance covered by B in one round = C = 3600 m
Time taken by B to complete one round = Distance/Speed = 3600/6 = 600 seconds
After A completes the first round in 900 seconds, she reverses direction and starts running anticlockwise. Now, both A and B are running in opposite directions.
Let's assume t is the time taken for A and B to cross each other for the first time.
In t seconds, A would have covered a distance of 4t in the clockwise direction, while B would have covered a distance of 6t in the anticlockwise direction. The sum of these distances should be equal to the circumference of the track.
So, we have the equation:
4t + 6t = C
Simplifying the equation:
10t = 3600
t = 3600/10
t = 360 seconds
Therefore, A and B will cross each other for the first time after 360 seconds.
Since the answer options are given in seconds, we need to convert 360 seconds into minutes. 360 seconds is equal to 6 minutes.
Hence, A and B will cross each other for the first time after 6 minutes, which is equal to 360 seconds. Thus, the correct answer is option 'c' (1080).
Let's assume the circumference of the circular track is C = 3600 m.
Calculating the time taken by A to complete one full round:
Speed of A = 4 m/s
Distance covered by A in one round = C = 3600 m
Time taken by A to complete one round = Distance/Speed = 3600/4 = 900 seconds
Calculating the time taken by B to complete one full round:
Speed of B = 6 m/s
Distance covered by B in one round = C = 3600 m
Time taken by B to complete one round = Distance/Speed = 3600/6 = 600 seconds
After A completes the first round in 900 seconds, she reverses direction and starts running anticlockwise. Now, both A and B are running in opposite directions.
Let's assume t is the time taken for A and B to cross each other for the first time.
In t seconds, A would have covered a distance of 4t in the clockwise direction, while B would have covered a distance of 6t in the anticlockwise direction. The sum of these distances should be equal to the circumference of the track.
So, we have the equation:
4t + 6t = C
Simplifying the equation:
10t = 3600
t = 3600/10
t = 360 seconds
Therefore, A and B will cross each other for the first time after 360 seconds.
Since the answer options are given in seconds, we need to convert 360 seconds into minutes. 360 seconds is equal to 6 minutes.
Hence, A and B will cross each other for the first time after 6 minutes, which is equal to 360 seconds. Thus, the correct answer is option 'c' (1080).
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Community Answer
Starting from the same point at the same time, A and B run on a 3600 m...
Given, speed of A = 4 m/s and Speed of B = 6 m/s
Length of track = 3600m
To complete 1 lap on the track, time taken by A = 3600/4 = 900 s
Similarly, time taken by B to complete 1 lap on track = 600 s
Now, by the time A completes 1 lap, B will have completed = 900/600 = 1.5 lap
Hence, after 900 seconds their position will be like the following:
Distance between A and B = 1800 m
Let A and B meet at a distance of x from B.
⇒ 4x = 6 × 1800 - 6x
⇒ 10x = 10800
⇒ x = 1080
∴ Time taken to travel x distance = x/6 = 1080/6 = 180 s
∴ Total time before A and B cross each other = 900 + 180 = 1080 s.
∴ After 1080 seconds of starting the run would they cross for the first time.
Length of track = 3600m
To complete 1 lap on the track, time taken by A = 3600/4 = 900 s
Similarly, time taken by B to complete 1 lap on track = 600 s
Now, by the time A completes 1 lap, B will have completed = 900/600 = 1.5 lap
Hence, after 900 seconds their position will be like the following:
Distance between A and B = 1800 m
Let A and B meet at a distance of x from B.
⇒ 4x = 6 × 1800 - 6x
⇒ 10x = 10800
⇒ x = 1080
∴ Time taken to travel x distance = x/6 = 1080/6 = 180 s
∴ Total time before A and B cross each other = 900 + 180 = 1080 s.
∴ After 1080 seconds of starting the run would they cross for the first time.
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Starting from the same point at the same time, A and B run on a 3600 m circular track with speeds of 4 m/s and 6 m/s, clockwise. After A completes the first round on the track, she reverses direction and runs anticlockwise. After how many seconds of starting the run would they cross for the first time?a)1200b)1620c)1080d)1020Correct answer is option 'C'. Can you explain this answer?
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