Foundation June 2019 Paper 1 Q23
23 A bus timetable shows the following information.
- A bus following route T leaves for the train station every 20 minutes.
- A bus following route A leaves for the airport every 18 minutes.
- A bus following route T and a bus following route A both leave at 8.37 am.
(a) When is the next time one of each bus is timetabled to leave at the same time? [4]
(b) Write down one assumption that was necessary to solve this problem. [1]
| Answer | Marks | Part marks and guidance |
|---|---|---|
| 11.37 [am] | 4 | B3 for 11.37 pm OR B2 for listing the next 3 correct times of both buses. i.e. 8.55, 9.13, 9.31 and 8.57, 9.17, 9.37 OR B1 for listing the next 3 correct times of one bus i.e. 8.55, 9.13, 9.31 or 8.57, 9.17, 9.37 Alternative method B3 for 3 [h] (must be sure 3 is not minutes) OR B2 for [LCM=] 180 or answer 14 37 or 2 37 pm OR M1 for [18=] \(2 \times 3^2\) or [20=] \(2^2 \times 5\) allow in a tree diagram etc or [LCM=] \(180k\) (\(k \ne 1\)) OR B1 for listing the next 3 multiples of 18 and 20 i.e. 36, 54, 72 and 40, 60, 80 See appendix for other methods |
Appendix
Q23
Alternative method
B1 for \(18x = 20y\)
B1 for \(x = 10\) \(y = 9\)
M1 for [837 +] \(\dfrac{10 \times 18}{60}\)
| Answer | Marks | Part marks and guidance |
|---|---|---|
| accept any correct assumption e.g. buses keep to the timetable or there are no delays or there are no changes to the timetable or they do not cancel any buses | 1 | See the appendix for other comments, if there is more than one comment mark the best one providing there are no incorrect comments |
Appendix
Exemplar responses for Q23(b)
| Response | Mark |
|---|---|
| buses keep to the timetable | 1 |
| buses arrive/leave on time | 1BOD |
| there are no delays | 1 |
| there are no unexpected stops | 1 |
| they follow the same routes each time | 1 |
| there are no changes to the timetable/ they keep to the timetable | 1 |
| they do not cancel any buses | 1 |
| no buses break down | 1 |
| there is no bad/heavy traffic | 1 |
| there is no traffic | 0 not enough |
| buses are travelling at constant speed | 0 |
| buses stop to recharge/ refuel or collect passengers | 0 |