Foundation June 2022 Paper 1 Q24
24 A machine can dig, on average, 2 cm of tunnel each minute.
It operates 24 hours each day.
(a) Work out how many days it should take to dig a tunnel of length 3.5 km.
Give your answer to the nearest day. [4]
Give your answer to the nearest day. [4]
(b) The machine actually digs an average of 2.5 cm of tunnel each minute for most of the time and an average of 1.5 cm each minute for the rest of the time.
How would this affect your answer to part (a)? [1]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 122 | 4 | B3 for 121.5[…] leading to an answer 121[.5…] or 1215.2[…] leading to an answer 1215 or 12.15[…] leading to an answer 12 | ignore any units throughout |
| OR M3 for \(\dfrac{3.5 \times 1000 \times 100}{2 \times 60 \times 24}\) oe | e.g. \(3500 \div 28.8\) M1 M1 may be implied by 0.0288 | ||
| OR M1 for correct time conversion to a day e.g. \([2 \times]\ 60 \times 24\) | M1 may be implied by e.g. 1440 or 14.4 or 0.0144 or 2880 or 28.8 | ||
| and M1 for one distance km to cm or one distance cm to km or two distances to metres | M1 may be implied by e.g. 0.02 and 28.8 or 3500 and (0.02 or 28.8) or 0.000 02 or 350 000 | ||
| and M1 for distance divided by rate e.g. \(\dfrac{3.5 \times 100 \times 100}{2 \times 60 \times 24}\) to a maximum of M2 | M1 may be implied by e.g. \(\dfrac{\textit{figs}\,35}{\textit{figs}\,288}\) or \(\dfrac{3.5 \times 1000 \times 100}{2 \times 60 \times 60 \times 24}\) or figs 175 | ||
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| It will take less time [than their 122 days] | 1 | accept any correct explanation (see appendix) and select best comment if more than one providing they do not conflict | |
Appendix
Exemplar responses for Q24b
| Response | Mark |
|---|---|
| it will take less time [than their 122 days] | 1 |
| my answer to part (a) will decrease | 1 |
| it will take longer on some parts and less time on other parts | 0 |
| it will increase | 0 |
| it will change the time | 0 |
| it will not affect my answer | 0 |
| it will take 4 days not 5 days (incorrect statement) | 0 |
| it make it faster to dig the tunnel | 0 |