Higher November 2017 Paper 2 Q13
13. Imran records details of his car journeys for 3 days.
| Day | Average speed | Time |
|---|---|---|
| Monday | 52 m.p.h. | 3 hours 30 minutes |
| Tuesday | 45 m.p.h | 2 hours 20 minutes |
| Wednesday | 44 m.p.h. | 1 hour 45 minutes |
| Total time: 7 hours 35 minutes | ||
You are given the following information.
- His car’s fuel consumption was 40 miles per gallon.
- 1 litre is approximately equal to 0·22 gallons.
- The cost of fuel is £1.25 per litre.
(a) Calculate the total cost of the fuel Imran used for the 3 days. [7]
(b) Imran usually spends a further 7 hours 35 minutes travelling in his car during the week.
(i) Give an estimate for Imran’s weekly fuel bill. [1]
(ii) Why might this estimate be unrealistic? [1]
| Scheme | Marks | Comments |
|---|---|---|
| May be completed for each of the 3 days separately | ||
| (Total distance =) \(52 \times 3\tfrac12 + 45 \times 2\tfrac13 + 44 \times 1.75\) \((= 182 + 105 + 77)\) | M2 | For M2 allow use of 2.33 for \(2\tfrac13\), but not 2.3 M1 for incorrect notation, 3(.)30 for 3.5 hours, 2(.)20 for 2 hours 20 minutes and 1(.)45 for 1 hour 45 minutes, OR M1 for any 1 of the 3 terms correct |
| 364 (miles) | A1 | CAO, do not accept 363.85 from use of 2.33 for \(2\tfrac13\) May be implied in further work |
| (Number of gallons of fuel used) \(364 \div 40\) AND (Number of litres used) \(\div\ 0.22\) (= 41.36... litres) | M2 | FT ‘their derived 364’ (= 9.1 gallons) M1 for \(364 \div 40\) or \(364 \div 0.22\) |
| (Cost is) \(41.36\ldots \times 1.25\) | m1 | FT provided the previous M2 awarded |
| (£) 51.7(0) | A1 | CAO, although accept answers in the range (£)51.62 to (£)52 inclusive |
| Scheme | Marks | Comments |
|---|---|---|
| (b)(i) Estimate (£)103.40 to (£)103.41 or (£)103 or (£)100 or (£)104 or (£)105 or (£)110 | B1 | Allow answers in the range (£)100 to (£)110 If an amount is not (£)103.40 to (£)103.41, then ‘their estimate’ must be a whole number of £s Similarly accept FT ‘2 × their (a)’ with an equivalent range |
| (b)(ii) Reason, e.g. ‘don’t know distance travelled’, ‘don’t know his speed for this other time’, ‘could be different fuel consumption’, ‘price of fuel might change’ | E1 | Do not accept, e.g. ‘because it is not accurate’ |
| (9) |