Speed, Distance and Time
Primary 6 · Mathematics
Speed, Distance and Time
Lesson 3 of 5
15 min
Let's begin
On sports day, Keza runs 100 m in 20 seconds. Mugisha runs 150 m in 25 seconds. They ran different distances, so who was faster? To compare them fairly, you need to know how far each one runs in one second. That is their speed.
Speed is the distance travelled in one unit of time. Keza covers 100 m in 20 s, so in 1 s she covers 100 ÷ 20 = 5 metres per second (5 m/s). Mugisha covers 150 ÷ 25 = 6 m/s. Mugisha was faster.
For long journeys we use kilometres per hour (km/h). A moto moving at 40 km/h would travel 40 km in one hour if it kept the same speed.
Worked example
(speed). A bus covers the 135 km from Kigali to Huye in 3 hours. Speed = 135 ÷ 3 = 45 km/h.
Worked example
(distance). A moto travels at 40 km/h for 1 h 30 min. First write the time in hours: 1 h 30 min = 1.5 h. Distance = 40 × 1.5 = 60 km.
Worked example
(time). How long does it take to drive 150 km at 60 km/h? Time = 150 ÷ 60 = 2.5 h = 2 h 30 min.
Speeds in km/h need the time in hours.
| Minutes | 15 min | 20 min | 30 min | 45 min |
|---|---|---|---|---|
| Hours | 0.25 h (14) | 13 h | 0.5 h (12) | 0.75 h (34) |
So 2 h 15 min = 2.25 h, not 2.15 h. Going the other way, 0.4 h = 0.4 × 60 = 24 min.
At a steady 60 km/h, distance and time grow together:
| Time | 0 | 15 min | 30 min | 1 h | 2 h |
|---|---|---|---|---|---|
| Distance | 0 | 15 km | 30 km | 60 km | 120 km |
Every column is the same rate of 60 km for each hour.
Worked example
A bus leaves Kigali at 07:30 and travels 135 km to Huye at 54 km/h. When does it arrive?
Time = 135 ÷ 54 = 2.5 h = 2 h 30 min. Arrival = 07:30 + 2 h 30 min = 10:00.
In the Unit Rates simulation, open the Racing Lab screen. Set a distance and a time for each car and watch which one wins. (The simulation measures distance in miles, but the idea is exactly the same as with kilometres.)
Tip
Draw a triangle with D on top and S and T side by side underneath. Cover the one you want: D = S × T, S = D ÷ T, T = D ÷ S.
Answers
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Quick check
A bus travels 240 km in 4 hours. What is its speed?
