perplexus.info :: Weights and Scales : The unplugged bath

The unplugged bath (Posted on 2002-07-03)

(This is an old chestnut of a puzzle, but with a slight twist)

It takes six minutes for just the cold tap to fill my bath with water.

The hot tap fills the bath at the same rate, but unfortunately (due to some strange plumbing) after the hot tap has been running for three minutes its supply of water shuts off for a full two and a half while the hot water tank refills and reheats - after the two and a half minutes, the hot tap commences dispensing water once again.

With the plug pulled out, a full bath empties (at a uniform rate) in only four minutes.

With the hot water tank full and the plug pulled out, how long will it take my bath to fill if I turn both taps on?

Submitted by Nick Reed

Rating: 3.1250 (8 votes)

Solution: (Hide)

The cold tap dispenses 1/6 of a bath-full of water every minute.
The hot tap similarly (when it is running).
The plug empties 1/4 of a bath-full every minute.
So, with both taps running and the plug out the bath fills by: 1/6 + 1/6 - 1/4 = 1/12 every minute
But, with only the cold tap running and the plug out, the bath loses: 1/4 - 1/6 = 1/12 every minute
So, for the first 3 minutes we gain (3 * 1/12). Then for the next 2.5 minutes (as the hot water tank refills and the hot tap is off) we lose (2.5 * 1/12).
So, over the first 5.5 minutes the bath fills by (3 * 1/12) - (2.5 * 1/12) = 1/24 of a bath-full.
At this point the tank is full once again, ready to restart this cycle.
So, an obvious solution to the problem would be to say it takes 24 * 5.5 minutes (132 minutes) to fill the bath.
This answer is wrong.
After 18 * 5.5 minutes, the tank is full, and the bath has 18/24 (9/12) of it's water in it.
For the next 3 minutes, both taps dispense water. We know this results in the bath filling by 1/12 every minute. So, after 3 more minutes the bath is full!
Total time: 18 * 5.5 + 3 = 102 minutes.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
No Subject	Hayden Franki	2024-10-04 16:48:15
Problem Solution With Explanation	K Sengupta	2007-05-16 11:11:48
some thoughts on the problem	K Sengupta	2007-05-12 15:54:49
re: Solution	vije	2004-07-02 15:01:50
1980 s	vije	2004-07-02 14:58:24
??	sharlene	2003-02-07 15:15:00
Solution	Hershel	2003-01-22 16:25:22
No Subject	Cory Taylor	2002-12-20 05:58:43
Solution	Justin	2002-07-03 07:43:10
re(3): Maybe...	Nick Reed	2002-07-03 07:31:30
re(2): Maybe...	Dulanjana	2002-07-03 07:13:07
re: Maybe...	Nick Reed	2002-07-03 06:32:22
Maybe...	Dulanjana	2002-07-03 06:30:15
Drowning caterpillar	Happy	2002-07-03 06:09:03
hmm (2)	Cheradenine	2002-07-03 05:54:02
Woop	Nick Reed	2002-07-03 05:26:53
re: Solution?	levik	2002-07-03 05:01:37
hmm..	Cheradenine	2002-07-03 04:35:30
Solution?	Dulanjana	2002-07-03 04:24:40

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