## Drain the dam brainteaser

By David Shaw, 12 May 2020

**Difficulty: Taxing**

Water engineers want to empty a dam to do repairs. There’s a creek running into the dam, which will keep filling the dam, unless they install pumps to empty that water. Each pump could empty a swimming pool in a week.

• If they use two pumps, it will take six weeks to empty the dam.

• If they use four pumps, it will take two weeks to empty the dam.

How many pumps do they need to empty the dam in one week?

**Scroll down or click for a hint, or the answer!**

## Brainteaser hint

Remember there’s a creek pouring more water into the dam all the time!

## Brainteaser answer

The first step is working out how much water comes down the creek.

To empty the dam with two pumps over six weeks, they would pump the equivalent of 2 x 6 = 12 swimming pools of water.

To empty the dam with four pumps over two weeks, they would pump 4 x 2 = 8 pools worth of water.

If the pumping takes four weeks longer (six weeks minus two weeks), the creek adds an additional four pools of water. That means the creek is adding one pool to the dam every week.

Over two weeks, they can pump eight pools of water. The creek adds two pools of water in that time, so the dam must hold the equivalent of six swimming pools.

To empty the dam in one week, the engineers would need six pumps, plus one pump to cover the water coming from the creek, for a total of seven pumps.

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