(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?

Let's examine a 24 gal tub. The cold and hot water are running at 4 gal/min. The drain is running out at 6 gal/min. With both drains on for the first the minutes, the taps will put 24 gal into the tub and the drain will remove 18 gal with a net of 6 gal in the tub for the 3 min cycle. In the next 2.5 min, the cold water will add 10 gal to the tub and the drain will take away 15 with a net of -5 gal in the tub for the 2.5 min cycle.

Following this line of thought.
Elapsed time -> Gallons of Water
3 min -> 6 gal
5.5 min -> 1 gal
8.5 min -> 7 gal
11 min -> 2 gal
14 min -> 8 gal
16.5 min -> 3 gal
.
.
.
93.5 min -> 17 gal
96.5 min -> 23 gal
99 min -> 18 gal
102 min -> 24 gal

Hence, the tub will fill up in 102 min

Posted by Justin on 2002-07-03 07:43:10