Higher June 2019 Paper 4 Q4
4 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 SC2 for answer 14 37 oe | |
Appendix: Question 4(a)
Alternative method :
B1 for \(18x = 20y\)
B1 for \(x = 10\) \(y = 9\)
M1 for [8 37 +] \(\frac{10 \times 18}{60}\)
| 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 Q4(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 |