Numeracy Higher June 2018 Unit 2 Q5
5. Hot water is often stored in cylinders.
The water in the cylinder is heated for use in the shower.
A plumbing engineer wants to calculate how long a shower can be used continuously before the water runs cold. He uses the following formulae:
\(C = \dfrac{H(X - M)}{M - Y}\) and \(T = \dfrac{C + H}{F}\)
Where:
\(C\) is the additional volume of water that feeds into the cylinder, in litres.
\(H\) is the volume of hot water that the cylinder holds, in litres.
\(M\) is the temperature of the water in the shower, in °C.
\(X\) is the temperature of the hot water in the cylinder, in °C.
\(Y\) is the temperature of the cold water that feeds into the cylinder, in °C.
\(T\) is the time spent using the shower before the water runs cold, in minutes.
\(F\) is the rate of flow of water in the shower, in litres per minute.
Daisy’s cylinder holds 300 litres of hot water.
The temperature of the hot water in her cylinder is 60°C.
The temperature of the cold water that feeds into Daisy’s cylinder is 8°C.
The water in Daisy’s shower is set at a temperature of 32°C.
Her shower has a rate of flow of 26 litres per minute.
Use the formulae to calculate
- the additional volume of water that feeds into Daisy’s cylinder, in litres,
- the number of minutes Daisy’s shower will run continuously before the water runs cold.
[5]
| Scheme | Marks | Comments |
|---|---|---|
| \(C = \dfrac{300 \text{ x } (60 - 32)}{32 - 8}\) | M2 | M1 for any 3 or 4 values substituted correctly |
| = 350 (litres) | A1 | CAO |
| \(T = \dfrac{350 + 300}{26}\) | M1 | FT ‘their derived 350’ and ‘their 300’ (used as H) |
| = 25 (minutes) | A1 | If no marks, award SC1 for all 5 of the following correctly matched, i.e. H = 300, M = 32, X = 60, Y = 8, F = 26 |