DISTANCE TIME GRAPH QUESTIONS

Problem 1 :

The graph alongside indicates the distance a homing pigeon travelled from its point of release until it reaches its home.

Use the graph to determine:

a. The total length of the flight

b. The time taken for the pigeon to reach home

c. The time taken to fly the first 200 km

d. The time taken to fly the from the 240 km mark to the 400 km mark

e. The average speed for the first 4 hours

f. The average speed for the whole flight

Solution :

a. Length of flight is 480 km.

b. Time to reach home is 10 hours.

c. Time taken for 240 km = 3 hours

Time taken for 1 km = 3/240

Time taken for 200 km = (3/240) x 200

= 2.5 hours.

d. It takes 3 hours to fly 240 km. it takes 6 1/2 hours to fly 400 km.

It takes 3 1/2 hours to fly from 240 km to 400 km.

e. In the first 4 hours it flies 320 km

Average speed = 320/4 = 80 km per hour.

f. It travels a distance of 480 km In 10 hours

Average speed = 480/10 = 48 km per hour.

Problem 2 :

The graph alongside indicates the distance a cyclist must travel to work. Use the graph to determine:

a. The distance to work

b. The time taken to get to work

c. The distance travelled after

i) 10 minutes    ii) 17 minutes

d. The time taken to travel

i. 6 km

ii.10 km

e. The average speed for the whole distance.

Solution :

a. The distance to work is 12 km.

b. Time taken to get to work is 26 km.

c.

i. The distance travelled after 10 minute is 4.5 km

ii. The distance travelled after 17 minute is 8.5 km

d.

i. The time taken to travel 6 km is 14 minutes

ii. The time taken to travel 10 km is 18.8 minutes

e.  

Average speed = total distance covered/total time taken

= 12/26 × 60

= 27.7 km per hour

Problem 3 :

Two rally cars were involved in a handicap time trial. The distance time graph indicates how far each has travelled.

Use the graph to determine:

a. The handicap advantage given to car Y

b. The distance travelled by each car

c. How far both cars had travelled when car X caught car Y

d. How long it took each car to travel 300 km

e. How much faster X completed the time trial than Y

f. The average speed of each car.

Solution :

a. By considering the the graph horizontally Car Y starts its travelling at 0, but Car Y starts after 40 minutes

So, the handicap advantage given to car Y is 40 minutes.

b. The distance travelled by each car is 390 km.

c. Far of both cars is approximately 280 km.

d. X car : 3 hours

    Y car : 4 hours

e. 1 hour  faster X completed the time trial than Y. 

f. X car :

Average speed = total distance covered/total time taken

= 390/4

= 97.5 km per hour

Y car :

Average speed = total distance covered/total time taken

= 390/5

= 78 km per hour

Problem 4 :

This graph shows the height of a balloon at different times.

a) From the graph, find the height of the balloon at 50 seconds.

b) Use the graph to find how long it took the balloon to rise from 30 meters to 60 meters.

Solution :

a) The height of balloon is 47 m when it is at 50 seconds.

b) For 30 meters height = 25 seconds

For 60 meters height = 80 seconds

= 80 - 25

= 55 seconds.

Problem 5 :

This graph shows how the temperature changed in Liam’s room one afternoon

a) Estimate the temperature at 3:15 pm.

b) Estimate the time when the temperature was highest.

c) How much did the temperature change from 2 pm to 2:30 pm? Give your answer to the nearest degree.

Solution :

a) The temperature is 22.5°C at 3:15 pm.

b) The temperature was highest at 2.48 pm.

c) At 2 pm, the temperature is 16.8°C approximately.

AT 2.30 pm, the temperature is 21.9°C approximately.

Temperature change = 21.9 - 16.8

= 5.1°C

Problem 6 :

150 people take part in a walk. This chart shows the number of people still walking at different times. 150 people take part in a walk. This chart shows

a) Use the chart to estimate the time when two-thirds of the people are still on the walk.

b) What percentage of the people who started are still on the walk at 3pm? What percentage of the people

Solution :

a) Total number of people = 150

= 2/3 of 150

= (2/3) x 150

= 100

b) Number of people walks at 3 pm = 30

Percentage of people who started at walk = (30/150) x 100%

= (1/5) x 100%

= 20%

Problem 7 :

This graph shows the temperature in a greenhouse.

a) Use the graph to find the time when the temperature was 25°C.

b) Use the graph to find the difference between the temperature at 2pm and the temperature at 4pm.

Solution :

a) The time is 3.15 pm when the temperature was 25°C

b) At 2 pm,

• the temperature is 20°C
• the temperature is 33°C

the difference = 33 - 20

= 13°C