Unit 3
4 marks · Normal(a) A train travels 45 km at a constant speed in 40 minutes. Calculate its average speed in km/h.
(b) On the axes below, sketch a possible distance–time graph for this journey.
(c) Solve the equation \( 2x = 7 - x \ ).
Calculate the average speed in km/h.
On the axes below, sketch a possible distance–time graph for this journey.
Solve \( 2x = 7 - x \ ) for x.
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
Show answer
(a) 67.5 km/h
(b) Straight increasing line from (0,0) to (40,45) · must show line from (0,0) to (40,45)
(c) x = 7/3 or 2.33 · must show x=7/3
Common mistakes: Not converting minutes to hours; Misreading graph axes; Incorrect solution for x
Show mark scheme and worked solution
Marking points
M1 (a) · 1 mark · Converts time to hours correctly (40 min = 2/3 hour).
A1 (a) · 1 mark · Finds average speed correctly (45 ÷ (2/3) = 67.5 km/h).
B1 (b) · 1 mark · Sketches correct straight line, origin to (40,45) or appropriate scaled axes.
A2 (c) · 1 mark · Solves for x: 2x = 7 - x; x = 7/3 or 2.33.
Worked solution
(a) 40 min = 2/3 hour. Speed = distance / time = 45 ÷ (2/3) = 45 × (3/2) = 67.5 km/h.
(b) Line starts at (0,0) and goes to (40,45) (straight, showing constant speed).
(c) 2x = 7 - x => 2x + x = 7 => 3x = 7 => x = 7/3 or 2.33.