Higher June 2024 Paper 3 Q6

(a) On Monday, Larrs swims 50 metres in 40 seconds at a constant speed.

On Tuesday, Larrs swims 1.5 kilometres.

Assume he swims at the same constant speed as on Monday.

How many minutes does he swim for on Tuesday? [5 marks]

(b) In fact, on Tuesday Larrs swims at a slower constant speed than on Monday.

What does this mean about the number of minutes he swims for on Tuesday?

Tick the correct box. [1 mark]

Mark scheme (a)

Answer	Mark	Comments
Alternative method 1: working in metres per second or kilometres per second
1500 (metres) or 0.05 (km)	B1	implied by 30 or 1200
their \(1500 \div 50 \times 40\) or \(1.5 \div\) their \(0.05 \times 40\) or 1200	M2	oe M1 their \(1500 \div 50\) or 30 oe or \(50 \div 40\) or 1.25 oe or \(1.5 \div\) their 0.05 oe their 1500 must be using digits 15 (and zeros) their 0.05 must be using single digit 5 (and zeros)
their \(1200 \div 60\)	M1dep	oe dep on M2
20	A1ft	ft their 1500 or their 0.05
Alternative method 2: working in metres per minute or kilometres per minute
1500 (metres) or 0.05 (km)	B1	implied by 0.075
\(40 \div 60\) or \(\dfrac{2}{3}\)	M1	oe accept [0.66, 0.67]
\(50 \div (40 \div 60)\) or 75 or \(\dfrac{\text{their } 0.05}{(40 \div 60)}\) or 0.075 or their \(1500 \times (40 \div 60)\)	M1dep	oe calculation their 1500 must be using digits 15 (and zeros) their 0.05 must be using single digit 5 (and zeros)
their \(1500 \div\) their 75 or \(1.5 \div\) their 0.075 or their \(1500 \times (40 \div 60) \div 50\)	M1dep	oe
20	A1ft	ft their 1500 or their 0.05

\(1500 \div 1.25\)	B1M2
\(1.5 \div 50 \times 40\) their 1500 must be using digits 15 (and zeros)	B0M2
\(1.5 \div 0.5 \times 40\) their 0.05 must be using single digit 5 (and zeros)	B0M2
\(150 \div 50\) their 1500 must be using digits 15 (and zeros)	B0M1
\(150 \div 1.25 = 120,\ 120 \div 60 = 2\)	B0M2M1A1ft