Topics › KS3 › Ratio & proportion
Speed
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A cyclist travels 6 km in 30 minutes. What is their average speed in km/h?
A
Option A:
0.2 km/h
B
Option B:
6 km/h
C
Option C:
3 km/h
D
Option D:
12 km/h
Answer and misconceptions
A
Option A:
0.2 km/h
✗
Uses minutes as if they were hoursWorks out 6 ÷ 30 without changing 30 minutes into 0.5 hours.
B
Option B:
6 km/h
✗
Gives the distance as the speedThinks travelling 6 km means 6 km/h, ignoring that it took only half an hour.
C
Option C:
3 km/h
✗
Multiplies distance by timeWorks out 6 × 0.5 (distance × time); speed is distance ÷ time = 6 ÷ 0.5.
D
Option D:
12 km/h
✓ Correct
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A train travels at 80 km/h for 3 hours. How far does it travel?
A
Option A:
240 km
B
Option B:
26.7 km
C
Option C:
83 km
D
Option D:
80 km
Answer and misconceptions
A
Option A:
240 km
✓ Correct
B
Option B:
26.7 km
✗
Divides speed by time to find distanceWorks out 80 ÷ 3; distance is speed multiplied by time.
C
Option C:
83 km
✗
Adds speed and timeCombines the two numbers by adding: 80 + 3.
D
Option D:
80 km
✗
Thinks the speed is the total distanceReads 80 km/h as 80 km in total, not 80 km in each hour.
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How long does it take to travel 150 km at 60 km/h?
A
Option A:
0.4 hours
B
Option B:
9000 hours
C
Option C:
2.5 hours
D
Option D:
90 hours
Answer and misconceptions
A
Option A:
0.4 hours
✗
Divides speed by distance to find timeWorks out 60 ÷ 150; time is distance divided by speed.
B
Option B:
9000 hours
✗
Multiplies distance by speed to find timeWorks out 150 × 60, not seeing that this cannot give a time.
C
Option C:
2.5 hours
✓ Correct
D
Option D:
90 hours
✗
Subtracts speed from distanceWorks out 150 − 60, combining the numbers without using the formula.
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A runner goes 10 km at 10 km/h, then another 10 km at 5 km/h. What is the average speed for the whole run?
A
Option A:
7.5 km/h
B
Option B:
$6\frac{2}{3}$ km/h
C
Option C:
$13\frac{1}{3}$ km/h
D
Option D:
60 km/h
Answer and misconceptions
A
Option A:
7.5 km/h
✗
Takes the mean of the two speedsAverages 10 and 5, but the runner spends longer (2 h) at the slower speed. Use total distance ÷ total time = 20 ÷ 3.
B
Option B:
$6\frac{2}{3}$ km/h
✓ Correct
C
Option C:
$13\frac{1}{3}$ km/h
✗
Works out time as speed ÷ distanceGets 10 ÷ 10 = 1 h and 5 ÷ 10 = 0.5 h, so 20 ÷ 1.5. Time is distance ÷ speed: 1 h + 2 h = 3 h.
D
Option D:
60 km/h
✗
Multiplies total distance by total timeWorks out 20 × 3 instead of 20 ÷ 3.
-
Which speed is the same as 36 km/h?
A
Option A:
600 m/s
B
Option B:
0.01 m/s
C
Option C:
$36\,000$ m/s
D
Option D:
10 m/s
Answer and misconceptions
A
Option A:
600 m/s
✗
Divides by 60 instead of 3600Changes km to m (36 000) but converts hours to minutes, not seconds.
B
Option B:
0.01 m/s
✗
Converts the time but not the distanceDivides 36 by 3600 but leaves the distance in km.
C
Option C:
$36\,000$ m/s
✗
Converts the distance but not the timeChanges 36 km to 36 000 m but leaves it per hour, not per second.
D
Option D:
10 m/s
✓ Correct