Speed, Distance and Time

Divide the total distance by the total time.

Distance is speed multiplied by time.

Time is distance divided by speed.

The units already match the requested speed unit.

Multiply the distance travelled each second by the number of seconds.

Divide by the number of minutes in one hour.

1. 45\div60=0.75 hour.

One whole hour contains 60 minutes.

1. 1.8\times60=108 minutes.
2. This is 1 hour 48 minutes, not 1 hour 80 minutes.

Convert the minutes to a fraction of an hour before dividing.

1. 24\div60=0.4 hour, so the total time is 1.4 hours.
2. 42\div1.4=30 km/h.

The distance divided by the speed gives hours. Convert that answer to minutes.

1. 90\div72=1.25 hours.
2. 1.25\times60=75 minutes.

Read the distance and time from the graph. Use hours for the time when finding km/h.

1. The graph shows 24 km travelled in 30 minutes.
2. 30\div60=0.5 hour.
3. Average speed =24\div0.5=48 km/h.

Convert the whole travel time to hours before multiplying by speed.

1. 12\div60=0.2 hour, so the time is 2.2 hours.
2. 55\times2.2=121 km.

Find the time in hours, then convert with 60.

1. 18\div7.5=2.4 hours.
2. 2.4\times60=144 minutes.

Work out the journey duration and add it to 13:40.

Part (a)

1. 126\div84=1.5 hours, or 1 hour 30 minutes.
2. 13:40 plus 1 hour 30 minutes is 15:10, so the hour part is 15.

Part (b)

1. 13:40 plus 1 hour is 14:40. Adding 20 minutes reaches 15:00; adding the remaining 10 minutes reaches 15:10. The minute part is 10.

Convert the distance and the time to the units named in the answer.

1. 1.5 km =1500 m and 2 minutes =120 seconds.
2. 1500\div120=12.5 m/s.

Work out the journey duration and arrival time, then compare the arrival with 09:45.

Part (a)

1. Travel time =27\div18=1.5 hours, or 90 minutes.
2. 08:20 plus 1 hour 30 minutes is 09:50.
3. The difference between 09:50 and 09:45 is 5 minutes.

Part (b)

1. The arrival time, 09:50, is after 09:45. The cyclist is 5 minutes late.

Use the distance travelled and the full elapsed time, including the horizontal section.

1. The graph ends at 90 km after 90 minutes. The driver travels away from home throughout the moving sections, so the total distance is 90 km.
2. The horizontal section is a stop. Its time is included in the 90 minutes.
3. 90\div60=1.5 hours. Overall average speed =90\div1.5=60 km/h.

Work out each journey time. Then divide total distance by total time.

1. Outward time: 60\div40=1.5 hours. Return time: 60\div60=1 hour.
2. Total distance: 60+60=120 km. Total time: 1.5+1=2.5 hours.
3. 120\div2.5=48 km/h.
4. The mean of 40 and 60 is not appropriate because more time is spent at the slower speed.

Find both travel durations, then add the waiting and walking time.

1. Bus time: 12\div24=0.5 hour =30 minutes.
2. Train time: 42\div84=0.5 hour =30 minutes.
3. Total time: 30+8+30+7=75 minutes, or 1 hour 15 minutes.
4. 07:50 plus 1 hour 15 minutes is 09:05. The commuter arrives 5 minutes after 09:00.

Find the time for each section before calculating the overall average.

1. Walking time: 2\div6=\frac13 hour, or 20 minutes.
2. Running time: 3\div10=0.3 hour, or 18 minutes.
3. Total distance is 2+3=5 km and total time is 20+18=38 minutes.
4. Average speed: 5\div(38\div60)=7.894736\ldots km/h.
5. To 1 decimal place, the average speed is 7.9 km/h.

Work out how long the first 60 km takes, then see how much of the 2 hours 30 minutes is left for the rest of the journey.

1. Time for the first section: 60\div40=1.5 hours.
2. Time allowed: 2 hours 30 minutes =2.5 hours.
3. Time left: 2.5-1.5=1 hour.
4. Distance left: 150-60=90 km.
5. Average speed needed: 90\div1=90 km/h.