Foundation November 2017 Paper 2 Q14

14 Halina cycled from A to B at an average speed of 26 km per hour.
She then cycled from B to C at an average speed of 20 km per hour.

Not to scale

She left A at 10.00 am, did not stop at B and arrived at C at 3.00 pm.

(a) It took Halina \(x\) hours to cycle from A to B.

(i) Explain why the distance from A to B, in kilometres, is \(26x\). [1]

(ii) Write down an expression, in terms of \(x\), for the time taken to cycle from B to C. [2]

(iii) Hence show that the distance from B to C, in kilometres, is \(100 - 20x\). [1]

(b) The total distance cycled by Halina from A to C is 118 km.

Find the distance from A to B. [4]

Mark scheme (a)

Answer	Marks	Part marks and guidance
(i) Valid explanation	1	Such as ‘distance is time times speed’	Need to see ‘multiply’ oe See Appendix
(ii) \(5 - x\)	2	M1 for time to travel from A to C = 5 [hours] soi	Must be seen in this part
(iii) \(20(5 - x) = 100 - 20x\)	1

Exemplar responses for Q14ai

Response	Mark
Because it’s the average speed x the number of hours it takes	1
Because the average speed to A to B was 26km per hour so it’s 26 x hours	1
Because you need to work at how many hours it took and times it by the speed	1
Because she cycled at 26 kmph and the x is how long it took so you multiply them (26kmph implies speed)	1 bod
Since to find the average speed you do distance x time so 26 x x \(\to\) 26x	0
Because she did 26 km per hour and we don’t know how many hours yet so we put x to show the number of hours	0
Because it’s 26x the 1 hour	0
Because her average speed is 26	0

Mark scheme (b)

Answer	Marks	Part marks and guidance
78	4	M1 for \(26x + 100 - 20x = 118\) M1 for their \(6x\) = their 18 M1 for \(x = \dfrac{\textit{their } 18}{\textit{their } 6}\) soi	Simplifying their equation to \(ax = b\) Simplifying their \(ax = b\) to \(x = \dfrac{b}{a}\)