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A and B walk around a circular track. A and B walk at a speed of 2 rounds per hour and 3 rounds per hour respectively. If they start at 8 a.m. from the same point in opposite directions, how many times shall they cross each other before 9.30 a.m.?
- a)5
- b)6
- c)7
- d)8
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
A and B walk around a circular track. A and B walk at a speed of 2 ro...
To solve this problem, we need to find out how many times A and B will cross each other before 9:30 a.m. Given that A walks at a speed of 2 rounds per hour and B walks at a speed of 3 rounds per hour, we can calculate the relative speed between A and B.
Relative speed = Speed of A + Speed of B
= 2 rounds per hour + 3 rounds per hour
= 5 rounds per hour
Since the track is circular, A and B will meet each other when they complete a total of one round. The time taken by A and B to complete one round can be calculated using the relative speed.
Time taken to complete one round = 1 round / Relative speed
= 1 round / 5 rounds per hour
= 1/5 hour
Converting 1/5 hour to minutes, we get:
1/5 hour * 60 minutes/hour = 12 minutes
So, A and B will cross each other every 12 minutes. We need to find out how many times they will cross each other before 9:30 a.m., which is 1 hour and 30 minutes after they start.
Total time = 1 hour + 30 minutes
= 1 hour + 30/60 hour
= 1.5 hours
Now, we can calculate the number of times they will cross each other by dividing the total time by the time taken to complete one round:
Number of crossings = Total time / Time taken to complete one round
= 1.5 hours / (1/5 hour)
= 1.5 * 5
= 7.5
Since we cannot have a fractional number of crossings, we round down to the nearest whole number. Therefore, A and B will cross each other 7 times before 9:30 a.m.
Relative speed = Speed of A + Speed of B
= 2 rounds per hour + 3 rounds per hour
= 5 rounds per hour
Since the track is circular, A and B will meet each other when they complete a total of one round. The time taken by A and B to complete one round can be calculated using the relative speed.
Time taken to complete one round = 1 round / Relative speed
= 1 round / 5 rounds per hour
= 1/5 hour
Converting 1/5 hour to minutes, we get:
1/5 hour * 60 minutes/hour = 12 minutes
So, A and B will cross each other every 12 minutes. We need to find out how many times they will cross each other before 9:30 a.m., which is 1 hour and 30 minutes after they start.
Total time = 1 hour + 30 minutes
= 1 hour + 30/60 hour
= 1.5 hours
Now, we can calculate the number of times they will cross each other by dividing the total time by the time taken to complete one round:
Number of crossings = Total time / Time taken to complete one round
= 1.5 hours / (1/5 hour)
= 1.5 * 5
= 7.5
Since we cannot have a fractional number of crossings, we round down to the nearest whole number. Therefore, A and B will cross each other 7 times before 9:30 a.m.
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Community Answer
A and B walk around a circular track. A and B walk at a speed of 2 ro...
Relative speed = Speed of A + Speed of B
(∴ they walk in opposite directions)
= 2 + 3 = 5 rounds per hour.
Therefore, they cross each other 5 times in 1 hour and 2 times in 1/2 hour
Time duration from 8 a.m. to 9.30 a.m. = 1.5 hour
Hence they cross each other 7 times before 9.30 a.m.
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A and B walk around a circular track. A and B walk at a speed of 2 rounds per hour and 3 rounds per hour respectively. If they start at 8 a.m. from the same point in opposite directions, how many times shall they cross each other before 9.30 a.m.?a)5b)6c)7d)8Correct answer is option 'C'. Can you explain this answer?
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