Question

Hi,
Pls help with this question. Thanks!

Ben and Sam started swimming at the same time from the opposite ends of a 30-m swimming pool. Each boy would turn in the opposite direction and continue swimming upon reaching the end of the pool. The average speed of Sam was 1 m/s and the average speed of Ben was 0.6 m/s. How many times did they meet each other if they swam for 10 min? (Assuming that the turning time is neglected.)

Sam will take 30 seconds to swim 1 lap whereas Ben will take 50 seconds to swim one lap. So in 10 minutes (600 seconds), Sam will swim 20 laps whereas Ben will swim 12 laps.

The tricky logic we need to understand here is, it does not matter whether they meet each other swimming in the same direction or in the opposite direction.

Since, Sam will definitely meet Ben for each lap that he swims, he will meet Ben a total of 20 times in 10 minutes.

Ans : 20

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Ben needs 30 seconds to swim from one end to the other end of the pool. Sam needs 50 seconds.

So they would have switched position after every 150 seconds.

Within each 150 seconds block, their distance versus time can be drawn like below (red is Ben, blue is Sam):

So their crossing is 5 times within each 150 seconds. After 10 mins, or 600 seconds, they would have crossed each other 5×4=20 times.

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16 times definitely

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I manually calculated this in a spreadsheet.

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Ans : 16 times.