Distance-Time Graphs

Worked example

1. 1

   $10:00\to 11:00=1\text{ h}$ — Take the first part of the line, before the stop. The time it lasts is the end time minus the start time.

2. 2

   $15-0=15\text{ km}$ — The distance gone is the end distance minus the start distance. Read both off the side scale.

3. 3

   $15÷1=15\text{ km/h}$ — Speed is distance divided by time.

4. 4

   $11:15\to 12:00=45\text{ min}=0.75\text{ h}$ — Now the part after the stop. Speed is in km per hour, so change 45 minutes into hours: 45 ÷ 60 = 0.75.

5. 5

   $24-15=9\text{ km}$ — The distance gone in this part: end distance minus start distance.

6. 6

   $9÷0.75=12\text{ km/h}$ — Speed is distance divided by time, using the time in hours.

7. 7

   $15>12$ — Compare the two speeds. The bigger speed is the steeper line.

8. 8

   $\text{Before the stop: its line is steeper}$ — Write the part AND the reason. The reason is what earns the mark.

Worked example

1. 1

   $12:00\to 12:45:\text{flat at }24\text{ km}$ — He rests for 45 minutes. A rest means the distance does not change, so draw a flat line at 24 km.

2. 2

   $\text{distance home}=24\text{ km}$ — The ride home must go all the way back to 0, so it covers the 24 km on the graph.

3. 3

   $24÷16=1.5\text{ h}$ — The question gives the speed, 16 km/h. Time is distance divided by speed.

4. 4

   $1.5\text{ h}=1\text{ h }30\text{ min}$ — 0.5 of an hour is half of 60 minutes, which is 30 minutes.

5. 5

   $12:45+1\text{ h }30\text{ min}=14:15$ — The ride home starts when the rest ends, at 12:45. Add the time it takes to get the arrival time.

6. 6

   $\text{line from }(12:45,24)\text{ to }(14:15,0)$ — Join the two points with a straight ruler line. It goes down to 0 because he is home again.

Worked example

1. 1

   $(12:45,24)\text{ and }(14:15,0)$ — Read the two ends of the straight part: the time and the distance at each end.

2. 2

   $24-0=24\text{ km}$ — The distance covered is the size of the change in distance. Going down still means 24 km travelled.

3. 3

   $14:15-12:45=1.5\text{ h}$ — The time taken is the end time minus the start time: 1 hour 30 minutes, which is 1.5 hours.

4. 4

   $24÷1.5=16\text{ km/h}$ — Speed is distance divided by time. Speed is never negative, even on the way back.

Worked example

1. 1

   $18+18=36\text{ km}$ — She goes out and comes back, so add both parts. The total distance travelled is not 0, even though she ends at home.

2. 2

   $1.5+0.5+1=3\text{ h}$ — Add all the times in hours: out 1.5, rest 0.5, back 1. The rest is included.

3. 3

   $36÷3=12\text{ km/h}$ — Total distance divided by total time.

Worked example

1. 1

   $12\times 2=24\text{ km at }12:00$ — Pick 12:00 for Asha, 2 hours after she starts. Distance is speed times time.

2. 2

   $44-20\times 1=24\text{ km at }12:00$ — Ben starts 44 km from A and moves towards A. In 1 hour he rides 20 km, so take it away from 44.

3. 3

   $(12:00,24)\text{ is on both lines}$ — Both are at the same time and the same distance from A, so the two lines cross at this point.

4. 4

   $\text{They meet at }12:00,24\text{ km from A}$ — Read the time from the bottom axis and the distance from the side axis.