Higher June 2017 Paper 4 Q9

9 Each week Dan drives two routes, route X and route Y.

One week he drives route X three times and route Y twice.
He drives a total of 134 miles that week.

Another week he drives route X twice and route Y five times.
He drives a total of 203 miles that week.

(a) Find the length of each route. [5]

(b) State an assumption that has been made in answering part (a). [1]

Mark scheme (a)

Answer	Marks	Part marks and guidance
24 31	5	M1 for \(3X + 2Y = 134\) oe M1 for \(2X + 5Y = 203\) oe	allow any correct method e.g. substitution
		M1 for multiplying both equations by scalars to equate coefficients of one variable (allow one arithmetic error) M1 for correct method to eliminate one variable (allow one arithmetic error)	M1 for rearranging one equation to make X or Y the subject, \(X = \frac{134 - 2Y}{3}\) M1 for substitution of their expression in the other equation
		if M4 not scored award B3 for one correct answer

Mark scheme (b)

Answer	Marks	Part marks and guidance
Any correct comment relating to distance	1		See appendix

Response	Mark
He does no other driving other than routes X and Y in the week	1
There are no diversions or detours	1
He sets off from the same place each time	1
That he only drives these two routes	1
They are the same 2 routes and never change	1
He could of gone to other routes as well as X & Y routes. He didn’t drive anywhere else.	1
That Dan isn’t driving anywhere else during the week	1
The routes are correctly measured	1
He takes exactly the same route each time.	1
He hasn’t taken any breaks	0
There are no stops	0
There is no traffic jams	0
He does not cancel his drive	0
That no stops in petrol stations were made	0
Y has a longer route than X	0
Dan prefers to drive route Y as he has driven it more than route X	0
He didn’t drive route X or Y there and back	0
That there is no traffic or road works	0