GRADE 9 Mathematics โ TIME,DISTANCE AND SPEED Quiz
1. A matatu travels 150 km in 3 hours. What is its average speed?
Average speed = total distance รท total time = 150 km รท 3 h = 50 km/h.
2. Convert 90 km/h into metres per second (m/s).
1 km/h = 5/18 m/s, so 90 km/h = 90 ร 5/18 = 25 m/s.
3. How long will it take to travel 36 km at a steady speed of 60 km/h?
Time = distance รท speed = 36 km รท 60 km/h = 0.6 h = 0.6 ร 60 = 36 minutes.
4. A runner completes 5 km in 25 minutes. What is the runner's speed in m/s (to two decimal places)?
5 km = 5000 m, 25 min = 1500 s. Speed = 5000 รท 1500 โ 3.333... โ 3.33 m/s.
5. A train covers 240 km in 2.5 hours. What is its average speed?
Average speed = 240 km รท 2.5 h = 96 km/h.
6. Convert 12 m/s to km/h.
1 m/s = 3.6 km/h, so 12 m/s = 12 ร 3.6 = 43.2 km/h.
7. Two towns are 180 km apart. A bus goes at 60 km/h while a car goes at 90 km/h. How much shorter is the car's journey time compared to the bus?
Bus time = 180 รท 60 = 3 h; car time = 180 รท 90 = 2 h; difference = 1 hour.
8. A person walks at 5 km/h. How long will it take to walk 2.5 km?
Time = distance รท speed = 2.5 รท 5 = 0.5 h = 30 minutes.
9. If you double your speed for a fixed journey, what happens to the time taken?
Time = distance รท speed. Doubling speed makes the denominator twice as large, so time becomes half.
10. A motorcycle travels 100 km at 50 km/h and another 100 km at 100 km/h. What is its average speed for the whole trip?
Total distance = 200 km. Time = 100/50 + 100/100 = 2 + 1 = 3 h. Average speed = 200 รท 3 โ 66.67 km/h.
11. Convert 7 minutes 30 seconds into seconds.
7 min 30 s = (7 ร 60) + 30 = 420 + 30 = 450 seconds.
12. A person increases walking speed from 4 km/h to 6 km/h. What is the percentage increase in speed?
Increase = (6 โ 4) รท 4 = 2 รท 4 = 0.5 = 50%.
13. A car travels 300 km. If the car uses fuel at the rate of 15 km per litre, how many litres are needed?
Fuel needed = distance รท rate = 300 km รท 15 km/l = 20 litres.
14. A cyclist rides at 15 km/h. How far does the cyclist go in 2 hours 20 minutes?
2 h 20 min = 2 + 20/60 = 2.333... h. Distance = speed ร time = 15 ร 2.333... = 35 km.
15. A bus leaves at 08:15 and arrives at 11:00. What is the duration of the journey?
From 08:15 to 11:00 is 2 hours 45 minutes.
16. A speedometer reads 72 km/h. What is this speed in m/s?
72 ร 5/18 = 72 ร 0.277... = 20 m/s.
17. A plane flies at 600 km/h. How long does it take to cover 1 200 km?
Time = distance รท speed = 1200 รท 600 = 2 hours.
18. Two people start towards each other from towns 80 km apart. One walks at 5 km/h and the other at 3 km/h. How long until they meet?
Relative speed = 5 + 3 = 8 km/h. Time = 80 รท 8 = 10 hours.
19. A car accelerates uniformly from 0 to 20 m/s in 10 seconds. What is its average speed during the acceleration?
With uniform acceleration, average speed = (initial + final) รท 2 = (0 + 20) รท 2 = 10 m/s.
20. A cyclist covers 24 km in 1 hour 30 minutes. What is the average speed in km/h?
1 h 30 min = 1.5 h. Average speed = 24 รท 1.5 = 16 km/h.
21. Convert 5 400 seconds into hours and minutes.
5 400 s รท 3600 = 1.5 h = 1 hour 30 minutes (note: 90 minutes is equivalent but the standard hours+minutes form is 1 hour 30 minutes).
22. Someone runs at 8 m/s. How many kilometres does he run in 1 minute?
Distance = speed ร time = 8 m/s ร 60 s = 480 m = 0.480 km = 0.48 km.
23. A car travels at 40 km/h for 30 minutes and then at 80 km/h for the next 30 minutes. What is the average speed for the whole 1-hour trip?
Distance1 = 40 ร 0.5 = 20 km; Distance2 = 80 ร 0.5 = 40 km; Total = 60 km in 1 hour โ average speed = 60 km/h.
24. A minibus leaves Nairobi at 09:20 and travels for 3 hours 40 minutes. At what time does it arrive?
09:20 + 3:40 = 13:00 in 24-hour time, which is 1:00 pm.
25. A person covers 15 km in 2 hours at a steady speed. How long will it take to cover 45 km at the same speed?
Speed = 15 รท 2 = 7.5 km/h. Time for 45 km = 45 รท 7.5 = 6 hours.