Suppose you have a water filled bucket with three holes. The first hole can empty the bucket in five minutes. The other hole can empty it in ten minutes. The last hole can empty it in 15 minutes. How long will it take for all three holes to empty the bucket? Please leave a comment if you have an answer or a guess.

## Sunday, February 25, 2007

### A Leaky Bucket

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## 4 comments:

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I'll take a stab at it.

The answer has to be less than 5 minutes, because the big hole will empty the bucket that fast, and we now have three holes pouring water (or whatever).

The second hole empties at half the rate of the big hole.

The third hole empties at 1/3 the rate of the big hole.

5min - (1/2)5min - (1/3)5min = x minutes

5min - 2.5min - 1.67min = 0.83minutes

0.83minutes = 49.8seconds to empty the bucket with all three holes involved.

Hmm... I think its 2.72 minutes

1st hole: 1/5 of bucket per minute

2nd hole: 1/10 of bucket per minute

3rd hole: 1/15 of bucket per minute

= 6/30 + 3/30 + 2/30

=11/30 bucket per minute

33/30 bucket = 3 minutes

30/30 bucket = 3 x 30 / 33

= 2.72 minutes

Correct!

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