a man was trying to swim to a buoy placed at a distance of 200m out in the sea. it took him 1 min to swim 20m. then a wave pushed him back 10m and he rested for about 1min before swimming again. he continued in his way for the rest of their journey. how long would it take the man to swim to the buoy?
effectively he gains 10 m every 2 minutes
but for the last 10 m he does not have to rest 1 minute to reach his goal.
That is, at the end of
2 minutes, he has gone 10 m
4 minutes, he has gone 20 m
...
36 minutes, he has gone 180 m
Since he can swim 20 m per minute, he will reach the 200 m after 37 minutes.
I did this same question last year in a slightly different way
http://www.jiskha.com/display.cgi?id=1420892277
notice the comment at the very end of that post.
To calculate the time it would take the man to swim to the buoy, we need to consider the distance covered in each swimming segment and account for the resting time. Let's break down the situation step by step:
1. The man swam 20m in 1 minute. So, his swimming speed is 20m per minute.
2. After swimming the initial 20m, a wave pushed him back 10m. Therefore, his net displacement is 20m - 10m = 10m.
3. The man rested for about 1 minute before swimming again.
4. From this point forward, the man continues swimming without any interruption, so we only need to calculate the time it would take for him to cover the remaining distance of 200m - 10m = 190m.
To find the time it takes to swim the remaining 190m, we can use the formula:
Time = Distance / Speed.
Since the swimming speed is 20m per minute, we have:
Time = 190m / 20m per minute = 9.5 minutes.
Adding the 1 minute for the initial swim and the 1 minute for the rest, the total time it would take the man to swim to the buoy is:
Total time = 1 minute (initial swim) + 1 minute (rest) + 9.5 minutes = 11.5 minutes.
Therefore, it would take the man 11.5 minutes to swim to the buoy.