Foundation November 2017 Paper 3 Q16
16 Chloe has a van.
She is going to use the van to deliver boxes.
Each box is a cuboid, 40 cm by 30 cm by 35 cm.
The space for boxes in the van has
| maximum length | 2.4 m |
| maximum width | 1.5 m |
| maximum height | 1.4 m |
The space for boxes is empty.
Chloe wants to put as many boxes as possible into the van.
She can put 3 boxes into the van in one minute.
Assume that the space for boxes is in the shape of a cuboid.
(a) Work out how many minutes it should take Chloe to put as many boxes as possible into the van. (4)
The space for boxes might not be in the shape of a cuboid.
(b) Explain how this could affect the time it would take Chloe to put as many boxes as possible into the van. (1)
| Answer | Mark | Notes |
|---|---|---|
| 40 | P1 | for the start of a process to find the number of boxes that will fit along one edge, eg. \(240 \div 40\ (= 6)\) or \(150 \div 30\ (= 5)\) or \(140 \div 35\ (= 4)\) or \(240 \div 30\ (= 8)\) or \(240 \div 35\ (= 6.85\ldots\) ie 6 boxes), etc. or for a process to find a volume, eg. \(40 \times 30 \times 35\ (= 42000)\) or \(0.4 \times 0.3 \times 0.35\ (= 0.042)\) or \(240 \times 150 \times 140\ (= 5040000)\) or \(2.4 \times 1.5 \times 1.4\ (= 5.04)\) NB: condone incorrect or no conversion between m and cm |
| P1 | for a complete process to find the maximum number of boxes, eg. \(\text{``}6\text{''} \times \text{``}5\text{''} \times \text{``}4\text{''}\ (= 120)\) or \(\text{``}5040000\text{''} \div \text{``}42000\text{''}\ (= 120)\) or \(\text{``}5.04\text{''} \div \text{``}0.042\text{''}\ (= 120)\) | |
| P1 | (dep on P1) for (their number of boxes) \(\div\, 3\), eg. \(120 \div 3\ (= 40)\) | |
| A1 | cao |
| Answer | Mark | Notes |
|---|---|---|
| explanation | C1 | for explaining that it could take more time or it could take less time with an appropriate reason, eg. “less space means less number of boxes which will take less time” or “it will take more time since a different arrangement would be required” |