Mon 16 Jun 2008
it’s not as difficult as it first looks:
Given two water faucets, one hot and one cold, and one bucket. The hot water fills the empty bucket in eight minutes. The cold water fills the bucket in seven minutes. Then I make a hole in the bucket such that the full bucket drains in four minutes. Now take the empty bucket, with the hole, and place under both faucets together. Turn on the hot and cold water at the same time. How long does it take to fill the bucket halfway?
June 16th, 2008 at 10:55 pm
quite long … there’s a hole in it
June 17th, 2008 at 1:21 am
How fast does the bathtub drain?
June 17th, 2008 at 7:14 am
Thank God for questions like this! I can’t tell you how many times this exact situation comes up for our developers.
June 17th, 2008 at 9:47 am
The interesting part is that the simplest symbolic solution uses the parallel operator I made my calculator learn after one too many classes on basic electronic devices:
R = R1 \\ R2 = 1 / (1/R1 + 1/R2)
June 17th, 2008 at 10:43 am
28 minutes?
(1/8 + 1/7) - 1/4 = speed while filling bucket
(7/56 + 8/56) - 14/56 = 1/56
So 56 minutes for the whole bucket, and 28 minutes for half a bucket. How close am I?
June 17th, 2008 at 11:40 am
good job Tristan! i solved it like this: (1/8)x+(1/7)x-(1/4)x=.5