Numeracy Higher June 2024 Unit 2 Q5
5. Caryl needs to calculate the cost of the petrol she used for a recent car journey.
She knows the following information about her journey:
- For part of her journey, she travelled a distance of 36 miles at a steady speed of 25 mph.
- For the rest of her journey, she travelled at a steady speed of 65 mph for 1 hour 24 minutes.
Some fuel economy information for her car is given in the following table:
| Speed | Number of miles travelled per gallon |
|---|---|
| 60 mph or less | 48 |
| Greater than 60 mph | 35 |
(a)
Calculate how many gallons of petrol Caryl used during her journey. [4]
(b)
Caryl paid £1.49 for each litre of petrol.
Calculate the cost of the petrol used for the journey. [3]
Remember:
1 gallon = 8 pints
| Scheme | Mark | Comments |
|---|---|---|
| (Number of gallons used =) \(\dfrac{36}{48}\) + \(\dfrac{65 \times 1\frac{24}{60}}{35}\) OR \(\dfrac{36}{48}\) + \(\dfrac{65 \times 1.4}{35}\) (= 0.75) (= 2.6) | M3 | Allow M2 for \(\dfrac{36}{48}\) + \(\dfrac{65 \times 1.24}{35}\) ( = 0.75 + 2.30…) OR sight of \(\dfrac{65 \times 1.4}{35}\) or equivalent M1 for sight of \(\dfrac{36}{48}\) or sight of 0.75 provided not from incorrect work Allow M1 for sight of \(\dfrac{65 \times 1.24}{35}\) OR \(\dfrac{65 \times 84}{35}\) (=156) |
| = 3.35 (gallons) | A1 | CAO Allow 3.4 (gallons) provided no incorrect work seen |
| Scheme | Mark | Comments |
|---|---|---|
| 3.35 × 8 ÷ 1.75 × 1.49 | M2 | FT ‘their 3.35 (gallons)’ from (a) Allow use of the conversion 1 litre = 1.75 to 1.76 pints M1 for the correct use of 3.35 with any 2 terms OR M1 for 8 ÷ 1.75 × 1.49 OR if one of the direct conversions from gallons to litres used as listed below, M1 for any one of the following:
|
| = (£)22.81(828...) or (£)22.82 | A1 | Must be from M2 Strict FT of their correct conversion between gallons and litres. Answers will be in the range (£)22.68 to (£)22.82 Allow the conversion into litres from any of the following also 1 pint = 568 to 572 ml 3.35 × 8 × (0.568 to 0.572) 1 gallon = 4.544 to 4.572 litres 3.35 × (4.544 to 4.572) 1 litre = 0.2187 to 0.22 gallons 3.35 ÷ (0.2187 to 0.22) |