Unit 9 Graphs 3 Q3a hint Draw horizontal axis from 9 am to 10 am and vertical axis from 0 to 8 km. Q3b hint How many 15 minutes are there in 60 minutes? This distance–time graph shows Isaac’s journey on his bicycle. Distance (km) 4 Reasoning Satbir leaves the house at 9 am. She cycles 5 km to town. It takes her 15 minutes. She goes to one shop for 30 minutes and then cycles 2 km further to her friend’s house. The journey to her friend’s house takes her 10 minutes. a Draw a distance–time graph for Satbir’s journey. b Work out the average speed in km per hour for each part of her journey. c Compare the average speeds to decide in which part of the journey she was cycling uphill. Isaac’s bike ride 160 140 120 100 80 60 40 20 0 8 am 9 am 10 am 11 am 12 am 1 pm 2 pm Time a How far did Isaac ride his bike on the first part of the journey? b At what time did he stop to rest? c How long did the first part of his journey take? d What was his average speed on the first part of the journey? e How many minutes did Isaac rest for? f How long did the last part of his journey take? g How far did he ride on the last part of the journey? h What was his average speed for the last part of the journey? Discussion What does the gradient of the line represent? How can you tell when Isaac was travelling fastest? Key point 7 5 This graph shows a fire engine’s journey to and from a fire. a Work out the average speed of the fire engine in km/h on the way to the fire. b For how long was the fire engine at the fire? c Work out the average speed of the fire engine in km/h on the way back to the fire station. d How far did the fire engine travel altogether? Discussion On a distance–time graph, what does a horizontal line represent? What about a negative gradient? Distance from fire station (km) On a distance–time graph the gradient represents the speed of the journey. 16 14 12 10 8 6 4 2 0 Journey to a fire 0 20 40 60 80 100 Time (minutes) Q5d hint The fire engine travels to the fire and back again. 259