### Brain Teasers

# Taps and Plugs

My bath has two taps and a plug hole. The cold tap on its own fills the bath in 15 minutes, the hot one in 6 minutes. The plug hole can drain the bath in 30 minutes with the taps off. How long will the bath take to fill if I leave both taps on with the plug left out?

### Answer

5 minutes1/15(Cold) + 1/6(Hot) = 1/x + 1/30

solve for x.

1/5 = 1/x =======> 5 minutes

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## Comments

you need to show your work please.

1/15 + 1/16 = 1/x - 1/30

slove for x.

1/5 = 1/x =======> 5 minutes

1/15 + 1/16 = 1/x - 1/30

slove for x.

1/5 = 1/x =======> 5 minutes

Nice teaser. Bad solution. (its just a time...no working)

A simple solution is to suppose the bath contains 30 litres. The cold tap fills at 2L/min, the hot tap fills at 5 L/min and the plughole drains at 1 L/min. Therefore the net inflow is 6 L/min. Hence 5 min.

t/15 + t/6 - t/30 = 1

(2t + 5t - t) / 30 = 1

6t = 30

(2t + 5t - t) / 30 = 1

6t = 30

In my head I did it as:

1 / (5/30 + 2/30 - 1/30) = 30/6 = 5

About 10 seconds.

1 / (5/30 + 2/30 - 1/30) = 30/6 = 5

About 10 seconds.

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