Sunday, February 25, 2007

A Leaky Bucket

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.


High Power Rocketry said...

: )

JAM said...

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.

The Minute Man: Colin Chang said...

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

Daniel Thompson said...