Tapping into mathematics

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# 5.7 Water, water everywhere

## Exercise 8

Before reading on, spend a few minutes making some notes about what information you would need to check the claim and how you would go about getting the information.

Write down what needs to be calculated, and how you would do the calculations.

Also, try to get a feel for the quantities involved. Start by asking yourself questions such as just how much water is likely to be lost if a tap drips for a week – would it be enough to fill a jug, a bucket, a bath or a swimming pool? How much does water cost, approximately? How much do nurses cost? How could you find out?

### Discussion

There is no single right way of tackling this investigation, but here is the approach of some of the authors.

Before tackling this question, it is a good idea to know roughly what quantities are being dealt with. We found that water is charged to hospitals in units of cubic metres (written as m3). That is quite a lot of water – 1 m3 of water is equivalent to 1000 litres. For comparison, a lavatory flush uses about 9 litres of water and an average bath uses roughly 90 litres. If you are more used to thinking in gallons, then one cubic metre of water is equivalent to about 220 imperial gallons, or about 90 household buckets.

Here are some other basic facts we decided we needed:

• What is a typical annual salary for a nurse? At the time of writing (1997) this is about £12,000. The annual cost (including pension costs and National Insurance) to a hospital of employing a nurse would be around £15,000.

• How fast does a tap drip? We started by assuming that a tap drips roughly once per second.

• What volume of water is this? To get a measure of the volume of water going down the drain we carried out a small experiment. We set a tap dripping and found that it took about 12 drops to fill a teaspoon. According to most cookery books, a teaspoon holds about 5 millilitres of liquid.

• How much does water cost? This is a hard question because it depends how it is being costed and indeed on who is paying for it. One local water authority suggested that, for a typical hospital in their region, a figure of about £0.91 per m3 would be appropriate.

• There are 1000 millilitres in 1 litre of water and 1000 litres in 1 cubic metre of water.

MU120_4MCAL