Speed is distance shared out over time
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.
Speed · A Car's Distance in 45 Minutes, and a Cyclist's Speed in Meters per Minute
QuestionA car traveled from Town P to Town Q at a steady speed of 72 km/h. The trip took 45 minutes. (a) How far is it from Town P to Town Q, in kilometers? (b) A cyclist took 3 hours to ride the same road. What was the cyclist's speed in meters per minute (m/min)?
1.72 km/h means the car covers 72 km in every hour, and an hour is 60 minutes.
72 km/h is 72 km in every hour, and an hour is 60 minutes. 2.Cut the hour into 4 equal parts of 15 minutes. In each 15 minutes the car covers 72 ÷ 4 = 18 km.
Cut the hour into 4 parts of 15 minutes: each part is 72 ÷ 4 = 18 km. 3.(a) 45 minutes is 3 of those parts, so the car covers 3 × 18 = 54 km. It is 54 km from Town P to Town Q.
45 minutes is 3 of those parts: 54 km. (a) 45 minutes is 54 km. 4.The cyclist rides the same 54 km. One kilometer is 1000 meters, so that is 54 × 1000 = 54000 m.
The cyclist rides the same 54 km, which is 54000 m, in 3 hours. 5.The cyclist takes 3 hours, so in each hour the cyclist rides 54000 ÷ 3 = 18000 m.
In each hour the cyclist rides 54000 ÷ 3 = 18000 m. 6.(b) An hour is 60 minutes, so in each minute the cyclist rides 18000 ÷ 60 = 300 m. The speed is 300 m/min. Check: in 3 hours, which is 180 minutes, the cyclist rides 300 × 180 = 54000 m.
(b) An hour is 60 minutes: 18000 ÷ 60 = 300 m/min.
Answer: (a) 54 km; (b) 300 m/min
Watch out for
- Multiplying the speed by the minutes: 72 × 45 = 3240 km. The speed is in kilometers per hour, so the time must be in hours: 45 minutes is 34 of an hour, and 72 × 34 = 54 km.
- Writing 45 minutes as 0.45 hours. An hour has 60 minutes, not 100, so 45 minutes is 45 ÷ 60 = 0.75 hours.
Your turn
1.120 km in 4 hours. Speed?