Higher June 2019 Paper 3 Q9
9 A company has to make a large number of boxes.
The company has 6 machines.
All the machines work at the same rate.
When all the machines are working, they can make all the boxes in 9 days.
The table gives the number of machines working each day.
| day 1 | day 2 | day 3 | all other days | |
|---|---|---|---|---|
| Number of machines working | 3 | 4 | 5 | 6 |
Work out the total number of days taken to make all the boxes. (3)
| Answer | Mark | Mark scheme |
|---|---|---|
| 10 | P1 | for a process to start to solve the problem eg \(6 \times 9\ (= 54)\) machine days needed or 12 (machine days used in first 3 days) or 42 (machine days needed after first 3 days) or 6 (machine days not used in first 3 days) or \(3 + 4 + 5\) equivalent to 2 days with 6 machines or has used 48 machine days in first 9 days |
| P1 | for \(\text{``}42\text{''} \div 6\ (= 7)\) (more days needed) or 3 days − 2 (equivalent) days (= 1) extra day needed to make up for the days not used | |
| A1 | cao |
Additional guidance
eg \(3 + 4 + 5\ (= 12)\)
eg \(6 \times 9 - 12\ (= 42)\)
eg \(3 + 2 + 1 = 6\)
eg \(12 \div 6 = 2\)