Higher November 2018 Paper 1 Q17
17.
Diagram not drawn to scale
At a factory, clay travels through a pipe with rectangular uniform cross-section measuring 25 cm by 12 cm.
The pipe is always full of clay which travels along the pipe at a constant speed of 5 cm per second.
How long does it take a 3-litre block of clay to travel completely through the 40 cm section of pipe from A to exit the pipe at B? [4]
| Scheme | Marks | Comments |
|---|---|---|
| (Flow \(= 25 \times 12 \times 5 =\)) 1500 (cm3/s) | B1 | |
| (3 litres takes) 2 (secs to exit pipe) | B1 | |
| (Takes \(40 \div 5 =\)) 8 (secs along pipe) | B1 | |
| (Total time \(= 2 + 8 =\)) 10 (secs) | B1 | FT ‘their 2’ + ‘their 8’ providing at least B2 previously awarded |
| (4) |
Alternative method 1
| Scheme | Marks | Comments |
|---|---|---|
| \(25 \times 12 \times \text{length} = 3000\) | B1 | |
| (Length =) 10 (cm) | B1 | |
| (Distance \(= 40 + 10 =\)) 50 (cm) seen or implied | B1 | |
| (Time taken \(= 50 \div 5 =\)) 10 (secs) | B1 |
Alternative method 2
| Scheme | Marks | Comments |
|---|---|---|
| (Whole pipe holds \(= 25 \times 12 \times 40 =\)) 12 (litres) or equivalent | B1 | |
| (Takes \(40 \div 5 =\)) 8 (secs along pipe) | B1 | |
| (3 litres takes) 2 (secs to exit pipe) | B1 | |
| (Total time \(= 2 + 8 =\)) 10 (secs) | B1 |