Higher June 2017 Paper 3 Q17

17 Liam drives his car.

He drives the first 9 miles in 9 minutes.
He then drives at an average speed of 70 miles per hour for 1 hour 36 minutes.

He finds this information about his car.

Average speed	Miles travelled per gallon
65 miles per hour or less	50
More than 65 miles per hour	40

Use the information to show that his car uses less than 3 gallons of petrol for the drive. [5 marks]

Mark scheme

Answer	Mark	Comments
Alternative method 1
1 mile per minute or 60 miles per hour or 0.15 (hours) or 1.6 (hours) or \(1\dfrac{36}{60}\) (hours)	B1
\(9 \div 50\) or 0.18	M1	oe
\(70 \times 1\dfrac{36}{60}\) or \(70 \times 1.6\) or 112	M1	oe
their \(112 \div 40\) or 2.8	M1dep	dep on 2nd M1
2.98 or 2.8 and (3 – 0.18 =) 2.82 or 0.18 and (3 – 2.8 = ) 0.2	A1	Ignore fw
Alternative method 2
1 mile per minute or 60 miles per hour or 0.15 (hours) or 1.6 (hours) or \(1\dfrac{36}{60}\) (hours)	B1
\(9 \div 50\) or 0.18	M1	oe
\(70 \times 1\dfrac{36}{60}\) or 112 or \(70 \times 1.6\) or 112	M1
\(40 \times (3 -\) their \(0.18)\) or 112.8	M1dep	dep on 1st M1
112.8 and 112	A1	Ignore fw
Alternative method 3
1 mile per minute or 60 miles per hour or 0.15 (hours) or 1.6 (hours) or \(1\dfrac{36}{60}\) (hours)	B1
\(9 \div 50\) or 0.18	M1	oe
\(70 \div 40\) or 1.75	M1
\(70 \div 40 \times 1.6\) or 2.8 or their \(1.75 \times 1.6\)	M1dep	oe eg 1.75 + 0.875 + 0.175 dep on 2nd M1
2.98 or 2.8 and (3 – 0.18 =) 2.82 or 0.18 and (3 – 2.8 = ) 0.2	A1	Ignore fw

Key facts are : First stage: Distance travelled 9 miles (given) Time taken 9 minutes (given) or 0.15 hours Average speed 60 mph Miles per gallon 50 mpg (given), Amount of petrol \(\;9 \div 50 = 0.18\) gallons Second stage: Distance travelled \(\;70 \times 1.6 = 112\) miles Time taken 1 hour 36 minutes (given) or 1.6 hours Average speed 70 mph (given) Miles per gallon 40 mpg (given), Amount of petrol \(\;112 \div 40 = 2.8\) gallons
An incorrect conversion of 1 hour 36 minutes to 1.36 can score: eg \(70 \times 1.36 = 95.2,\ 95.2 \div 40 = 2.38\) \(70 \times 1.36 = 95.2,\ 95.2 \div 40 = 2.38,\ 0.18 + 2.38 = 2.56\)	B0M0M1M1A0 B1M1M1M1A0
2.98 = 3 (further work)	B1M1M1M1A1
\(9 \div 50\)	B1M1