# Bath Filling Quiz Puzzle

This week’s puzzle is split into two parts: the first is an old puzzle that many might not have seen, and is worth a look in its own right; however the second part is new, and is slightly trickier.

The problem concerns a bath. With the plug in and the cold tap turned on full the bath will fill in three minutes. The hot tap is slightly slower, and with the plug in and the tap on full the bath will fill in four minutes. With the taps off a full bath will empty in twelve minutes when the plug is removed.

So how long will it take to fill the bath with both taps on full and the plug removed?

Assuming that you have solved this part, the trickier subsidiary is . . .

If the bath starts half full how long will it take to fill completely if both taps are turned on full and the plug is removed?

• Quiz Master Shop

The water will go down the plughole faster when the bath’s full

• Rich Twose

Am I missing something? Seems to me like it would fill in 2 minutes and 1 minute respectively.

I am making a couple of assumptions – the water has a negilible travel time from tap to bath, and that the plug is removed at the same time the taps are turned on (more relevant for the second scenario). Also, running hot and cold together doesn’t have a net loss on flow rate (it certainly was the case in my last house…)

If we take the time to drain as our reference, it drains 1/12th per minute. Using the same scale, the cold tap fills it 4/12ths a minute, and the hot is 3/12ths. Combined, hot and cold will fill it 7/12ths a minute.

7/12ths – 1/12th = a net 6/12ths a minute fill rate, after factoring in the drain. This means you should be hitting 12/12ths at the 2 minute marks.

For the half full scenario, I am assuming we aren’t factoring in fluid dynamics etc and increased pressure at the plug hole as the level rises. This means we start at 6/12ths so only need to add the same again, which would take a minute.