Tapping into mathematics
Tapping into mathematics

Start this free course now. Just create an account and sign in. Enrol and complete the course for a free statement of participation or digital badge if available.

Free course

Tapping into mathematics

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?


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.


Take your learning further

Making the decision to study can be a big step, which is why you'll want a trusted University. The Open University has 50 years’ experience delivering flexible learning and 170,000 students are studying with us right now. Take a look at all Open University courses.

If you are new to University-level study, we offer two introductory routes to our qualifications. You could either choose to start with an Access module, or a module which allows you to count your previous learning towards an Open University qualification. Read our guide on Where to take your learning next for more information.

Not ready for formal University study? Then browse over 1000 free courses on OpenLearn and sign up to our newsletter to hear about new free courses as they are released.

Every year, thousands of students decide to study with The Open University. With over 120 qualifications, we’ve got the right course for you.

Request an Open University prospectus371