Graphs 3
4 marks · HardA distance–time graph for two people, Amira and Ben, is shown below. Both walk from the same starting point to the same destination.
a) Compare the journey times for Amira and Ben to reach the destination.
b) Find the time interval during which Ben is stationary and work out how far he is from the start during this time.
c) Calculate the speed (in km/h) for Amira over her whole journey.
Time taken for Amira (min):
Time taken for Ben (min):
Ben stationary from minute ___ to ___. Distance from start (km):
Speed of Amira (km/h):
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) Amira: 16 minutes; Ben: 22 minutes
(b) From 6 min to 12 min; distance = 0.8 km
(c) 9 km/h
Common mistakes: Incorrect conversion of minutes to hours; Wrong reading of stationary section; Ignoring units
Show mark scheme and worked solution
Marking points
B1 (a) · 1 mark · Correctly states journey times for Amira (16 min) and Ben (22 min).
B1 (b) · 1 mark · Identifies Ben is stationary between 6 minutes and 12 minutes, distance is 0.8 km from start.
M1 (c) · 1 mark · Correctly converts 16 minutes to hours (16/60 = 0.267 h) and sets up speed calculation.
A1 (c) · 1 mark · Correctly calculates Amira's speed as 9 km/h to 1 decimal place (accept any answer between 8.95 and 9.05).
Worked solution
a) Amira reaches 2.4 km at 16 min. Ben reaches 2.4 km at 22 min. So Amira: 16 min, Ben: 22 min.
b) Ben is stationary from 6 min to 12 min at a distance of 0.8 km (horizontal section of Ben's graph).
c) Amira's speed = 2.4 km / (16/60) h = 2.4 / 0.267 = 9 km/h.