# Water Tank Quiz Puzzle

There's a well-known puzzle about a bath with hot and cold taps that work at different rates, and a plughole that empties the bath. Well, we have for you a similar puzzle about a water tank.

Using a bucket and carrying water from a nearby pond, Fred can fill the water tank in ten minutes.

Using the same bucket and water source John can fill the water tank in four minutes.

However, John works twice as fast as Fred works! This would seem incorrect, as you would think that the times should be five minutes and ten minutes or four minutes and eight minutes.

The reason for this apparent discrepancy is the hole in the water tank. Fred has to overcome more leakage than John, hence his time is more than twice as long.

The question is not how long the men take to fill the water tank, the question is how long does it take for a full water tank to leak away and become an empty water tank.

## 1 comment

• philip smith

If Fred fills the bath at L litres per min
Then, John fills the bath at 2L litres per min.
If the run off rate from the hole is R litres per min then,
Fred takes 10 min to fill the bath so volume of water in the bath is 10L-10R
John takes 4 min to fill the bath so volume of water in the bath is 8L-4R

Hence 10L-10R=8L-4R

This gives L=3R and hence volume of water in the bath is 20R.

Time taken for bath to empty is
20R÷R= 20 minutes