How far in each hour
A car travels 120 km, and the trip takes 4 hours. How fast was the car going? Speed measures how far something travels in each unit of time, so the question is really: how many kilometers did the car travel in each hour?
The whole trip of 120 km, cut into the 4 hours it took.
Share the distance between the hours
Suppose the car went at a steady speed, so it covered the same distance in every hour. Then the 120 km is shared equally between the 4 hours: 120 ÷ 4 = 30 km in each hour. The car's speed is 30 kilometers per hour, written 30 km/h.
So speed = distance ÷ time. The unit of a speed names both quantities: km/h means kilometers per hour, a distance for each unit of time.
Each hour of the trip covers 120 ÷ 4 = 30 km, so the speed is 30 km/h.
Speed is a rate
A speed is a rate, so rate × units = total works for it too. Here the rate is the speed, the units are hours and the total is the distance: distance = speed × time. At 30 km/h, the car travels 30 × 5 = 150 km in 5 hours.
Dividing the other way gives the time: time = distance ÷ speed. At 30 km/h, a trip of 90 km takes 90 ÷ 30 = 3 hours.
At 30 km/h, every hour adds 30 km: 90 km sits under 3 hours and 120 km under 4 hours.
Minutes in a speed per hour
A speed in km/h counts kilometers in a whole hour, so a time in minutes must be changed into hours first. There are 60 minutes in an hour, so 30 minutes is hour and 15 minutes is hour.
A cyclist rides at 40 km/h for 15 minutes. 15 minutes is hour, so the cyclist rides km. In 45 minutes, which is hour, the cyclist rides 3 × 10 = 30 km.
At 40 km/h, the 40 km of one hour is shared between four lots of 15 minutes, so each 15 minutes covers 10 km.
The usual mistakes
Giving the distance as the speed. 120 km in 4 hours is not 120 km/h: that would be 120 km in one hour. The trip took 4 hours, so divide: 120 ÷ 4 = 30 km/h.
Multiplying the speed by the minutes. At 40 km/h for 15 minutes, 40 × 15 = 600 km is far too far. Change the 15 minutes into hour first.
Worked example: Direct Formula Application with Unit Conversion
Question A motorist traveled from Town P to Town Q at a constant speed of 72 km/h. The journey took 45 minutes. (a) What was the distance between Town P and Town Q in kilometers? (b) A cyclist took 3 hours to cover the same distance. Find the cyclist's speed in meters per minute (m/min).
1.Speed is 72 km per 60 minutes.
Speed is a distance per hour: 72 km in 60 minutes. 2.Split 60 minutes into 4 units of 15 minutes: 1 unit (15 min) = 72 ÷ 4 = 18 km.
Cut the hour into quarters: 15 minutes is 72 ÷ 4 = 18 km. 3.(a) 45 minutes = 3 units = 3 × 18 km = 54 km.
45 minutes is 3 of those units: 54 km. (a) 45 minutes is 54 km. 4.Represent cyclist's distance: 54 km = 54000 m.
The cyclist covers the same 54 km, which is 54 000 m, in 3 hours. 5.Cyclist covers 54000 m in 3 hours ⟹ 1 hour = 54000 ÷ 3 = 18000 m.
One hour of cycling is 54000 ÷ 3 = 18000 m. 6.(b) Divide 1 hour into 60 minutes: 18000 m ÷ 60 = 300 m/min.
(b) An hour is 60 minutes: 18000 ÷ 60 = 300 m/min.
Answer: (a) 54 km; (b) 300 m/min
Common mistakes
- Multiplying speed directly by minutes: 72 × 45 = 3240 km.
- Converting 45 minutes incorrectly as 0.45 hours instead of 0.75 hours.
- Dividing 54 km by 3 h to get 18 km/h and forgetting to convert to m/min.