1. Mathematics
Compound Units - Speed

2. Lesson Objectives The aim of this powerpoint is to help you…
Use the link between speed, distance and time to solve problems

3. Compound Measures
Compound measures are measurements involving more than one type of unit
Speed is an example of a compound measure.
It could be measured in miles per hour.
It is therefore a mix (or compound) of distance (or length) (e.g. miles) and time (e.g. hours)
The ‘per’ in-between the miles and the hour shows you divided a distance by a time to get a speed.

4. Formula Triangles y z In this triangle…
To help re-arrange formulas involving exactly three variables and only division or multiplication, we can use a formula triangle
To use them, cover the variable you want to find with your thumb and work out the formula as follows:
The top value is divided by either of the bottom values or the bottom values are multiplied together.
In this triangle…
cover x to find it equals yz (on the bottom), ie x = yz
cover y to find it equals x on the top divided by z on the bottom, ie y=x/z and so on… x
y z

5. Speed, Distance and Time
To find the formula triangle for speed, distance and time, look for the units of the compound measure
Speed can be measured in metres per second
Thus: Speed = distance ÷ time
Divide TOP by BOTTOM

6. SDT Formula Triangle Formulae: S = D ÷ T D = ST (ie. S × T) T = D ÷ S
Don’t forget to cover the
letter of the variable you
are trying to find!

7. Units
When answering questions please be careful about the units you use they must be compatible!
If your distance is metres and time is seconds then the speed units are metres per second
If your speed is in km per hour and distance is in km, then time is in hours
If time is in hours and speed is in metres per minute, then a conversion is needed before calculating distance and its units!

8. SDT Problems – Quick Practice
What speed am I travelling at if I travel 90 miles in 3 hours?
How long does it take to travel 140 miles at an average speed of 40mph?
How far can you travel in 3 hours at an average speed of 56 miles per hour?
Work out your answers before clicking on to the next slide

9. SDT Problems - Answers
What speed am I travelling at if I travel 90 miles in 3 hours?
S = D ÷ T  90 miles ÷ 3 hours = 30 mph
How long does it take to travel 140 miles at an average speed of 40mph?
T = D ÷ S  140 miles ÷ 40mph = 3½ hrs
How far can you travel in 3 hours at an average speed of 56 miles per hour?
D = S × T  56mph × 3h = 168 miles

10. Compound Measure Conversions
Step-by-Step guide to converting:
(1) (Use the formula triangle to) write out the formula including units
(2) Convert each unit as required
(3) Carry out the calculation

11. Conversions – Example 1 Change 36km per hour to metres per second
(1) Speed = distance ÷ time
Speed = 36km ÷ 1 hour
(2) (36 km  m) (1 h  60 m  3600s)
(3) Speed = m ÷ 3600 s = 10m/s

12. What next?
Print out the notes called Speed. Read through them and make sure you answer any questions.
Work through the MyMaths lesson and its online homework called Speed found at:
Save and complete the worksheet: SDT-S1.xlsx
Now move on to the PAV1 powerpoint