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DIRECTIONS for questions 9 and 10: Type in your answer in the input box provided below the question. Two persons, A and B, simultaneously started running, from the same point, around a circular track, in the same direction, and met each other for the first time after 15 min from the start, during which time B had completed exactly five laps. Instead, if they had run in opposite directions, after how many minutes from the start would their 11th meeting have taken place, given that the speed of A is more than the speed of B?

Question

DIRECTIONS for questions 9 and 10: Type in your answer in the input box provided below the question. Two persons, A and B, simultaneously started running, from the same point, around a circular track, in the same direction, and met each other for the first time after 15 min from the start, during which time B had completed exactly five laps. Instead, if they had run in opposite directions, after how many minutes from the start would their 11th meeting have taken place, given that the speed of A is more than the speed of B?

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Solution

The problem can be solved in the following steps:

Step 1: Understand the problem The problem states that two people, A and B, are running on a circular track. B completes 5 laps in 15 minutes. We need to find out when their 11th meeting would be if they were running in opposite directions, given that A is faster than B.

Step 2: Calculate the speed of B Since B completes 5 laps in 15 minutes, the speed of B is 5 laps/15 minutes = 1/3 laps per minute.

Step 3: Calculate the speed of A Since A and B meet for the first time after 15 minutes while running in the same direction, this means that in 15 minutes, A has completed one more lap than B. So, the speed of A is (5+1) laps/15 minutes = 2/5 laps per minute.

Step 4: Calculate the time of their 11th meeting if they were running in opposite directions When two people run in opposite directions, their speeds are added. So, the combined speed of A and B is 2/5 laps per minute + 1/3 laps per minute = 11/15 laps per minute. This means they meet once every 15/11 minutes. Therefore, their 11th meeting would be after 15/11 minutes * 11 = 15 minutes.

This problem has been solved

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