Numeracy Higher June 2018 Unit 1 Q9
9. Matas knows the following information about the amount of fuel his car uses.
| Speed | Miles per gallon |
|---|---|
| 30 mph | 54 |
| 50 mph | 60 |
| 70 mph | 50 |
During one journey, Matas drove at 50 mph for part of the time and at 70 mph for the rest of the time.
He drove for 3 hours at a speed of 50 mph.
For the whole journey, Matas used 4·6 gallons of fuel.
For how long did Matas travel at 70 mph?
You must show all your working. [6]
| Scheme | Marks | Comments |
|---|---|---|
| (Fuel used at 50 mph =) (50 × 3) ÷ 60 | M1 | |
| = 2·5 (gallons) or equivalent | A1 | |
| (Fuel used at 70 mph = 4·6 – 2·5) = 2·1 (gallons) | B1 | FT ‘their derived 2·5’ provided < 4·6 |
| (Dist travelled at 70 mph = 2·1 × 50) = 105 (miles) | B1 | FT 'their 2·1' |
| (Time travelling at 70 mph =) 105 ÷ 70 | M1 | FT ‘their 105’ provided an attempt has been made to use ‘their 2·1' to find the distance travelled at 70 mph |
| = 1·5 hours or equivalent | A1 | CAO |