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

	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.

	Subject	Author	Date
	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