Year 7 · Speed, distance and time
Swap between milliseconds, seconds, minutes and hours
Learn how to convert between units of time, use timetables and calendars, and link speed, distance and time, in calculations and on a graph.
Definition
Time is measured in units that build on each other: 1000 milliseconds make a second, 60 seconds a minute, 60 minutes an hour and 24 hours a day. Once you can move between those units, time becomes something you can calculate with, in timetables, on the calendar, and in the relationship speed = distance ÷ time. A speed is a rate: it says how much distance is covered in each unit of time, which is why a distance-time graph shows speed as steepness.
Why Do I Have to Learn This?
Telling the time keeps your whole day organised. Clocks, timetables and cooking timers all depend on it.
Key Rules:
- 1. Convert time units by multiplying or dividing by the right factor: 1000 milliseconds make a second, 60 seconds make a minute, 60 minutes make an hour and 24 hours make a day.
Remember:
- •Speed = distance ÷ time, with matching units. On a distance-time graph, steepness is speed.
Don’t Forget...
- •Treating 2.30 on a calculator as 2 hours 30 minutes. Time is not decimal: 30 minutes is 3060 of an hour, so 2 hours 30 minutes is 2.5 hours, not 2.3 hours.
- •Dividing time by distance when finding a speed. Speed compares distance per unit of time, so the distance goes on top: 135 ÷ 2.5 gives miles per hour, while 2.5 ÷ 135 gives hours per mile, a different quantity.
- •Reading a steep section of a distance-time graph as a hill. The vertical axis shows distance from the start, not height, so a steep section means a lot of distance in little time, which is high speed, and a horizontal section means stopped.
Analogue clock
A clock with hands that move round a numbered face.
When the small hand points to 3 and the big hand to 12, the time is 3 o’clock.
Worked Example:
A coach travels 135 miles in 2 hours 30 minutes. Work out its average speed in miles per hour.
Change the time into hours: 30 minutes is 3060 = 0.5 hours, so 2 hours 30 minutes is 2.5 hours.
Use speed = distance ÷ time: speed = 135 ÷ 2.5.
135 ÷ 2.5 = 54. Check by reversing: 54 × 2.5 = 135 miles.
Answer: 54 miles per hour
Why It Works:
Speed is defined as the distance covered in one unit of time, so dividing the whole distance by the whole time, in matching units, gives the distance covered in each single hour. Because speed × time = distance is one fixed relationship, knowing any two of the three values determines the third.
Another Example:
A distance-time graph shows a cyclist ride 20 km in the first hour, rest for half an hour, then ride a further 15 km in the final half hour. What is the fastest speed the graph shows?
Work out the gradient of each sloping section. The first section covers 20 km in 1 hour, so its speed is 20 ÷ 1 = 20 km/h.
The middle section is horizontal: the distance does not change, so the cyclist is stopped.
The final section covers 15 km in 0.5 hours, so its speed is 15 ÷ 0.5 = 30 km/h.
The final section is the steepest, so it shows the fastest speed.
Answer: 30 km/h, on the final section
Animated Example:
Free Swap between milliseconds, seconds, minutes and hours Worksheet
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Before this: Converting units (Year 6) · Next: Proportion and scale (Year 8)
Let’s Practise the Concept
Step 1 of 3
Put them in order
Tap the numbers from smallest to largest.
In order so far: nothing yet