Compound Measures

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Speed — Distance — Time

A compound measure involves two different units combined, such as metres per second or kilometres per hour. Speed measures how far something travels in a given time.

Speed = Distance ÷ Time
Distance = Speed × Time
Time = Distance ÷ Speed

How to use the triangle:
Cover the quantity you want to find. What remains shows the calculation:
• Cover D → you see S × T
• Cover S → you see D ÷ T
• Cover T → you see D ÷ S

Common units: mph (miles per hour), km/h, m/s

📝 Example 1: Finding speed

Given

A car travels 180 km in 2.5 hours. What is its average speed?

Formula

Speed = Distance ÷ Time

Calculate

Speed = 180 ÷ 2.5 = 72 km/h

Average speed = 72 km/h

📝 Example 2: Finding distance

Given

A train travels at 80 km/h for 2.5 hours. How far does it travel?

Calculate

Distance = Speed × Time = 80 × 2.5 = 200 km

Distance = 200 km

📝 Example 3: Finding time

Given

How long does it take to travel 240 miles at 60 mph?

Calculate

Time = Distance ÷ Speed = 240 ÷ 60 = 4 hours

Time = 4 hours

⚠ Units warning: Make sure your units match. If speed is in km/h, distance must be in km and time in hours. Convert first if needed. 20 minutes = 20 ÷ 60 = 1/3 hour.

📝 Example 4: Unit conversion before calculating

Given

A cyclist travels 18 km in 45 minutes. Find their speed in km/h.

Step 1 — Convert time

45 minutes = 45 ÷ 60 = 0.75 hours

Step 2 — Calculate

Speed = 18 ÷ 0.75 = 24 km/h

Speed = 24 km/h

✓ Quick Check 1 — Speed, Distance and Time

Question 1 of 10

Density — Mass — Volume

Density measures how much mass is packed into a given volume. A material with high density (like iron) is heavy for its size; low density (like wood) is light for its size.

If density > 1 g/cm³, the object sinks in water. If density < 1 g/cm³, it floats.

Density = Mass ÷ Volume
Mass = Density × Volume
Volume = Mass ÷ Density

Real example — iron:
Density of iron = 7.87 g/cm³
Mass of iron block = 200 g
Volume = 200 ÷ 7.87 = 25.4 cm³

Common units: g/cm³ or kg/m³

📝 Example 5: Finding density

Given

A metal block has a mass of 540 g and volume of 60 cm³. Find its density.

Calculate

Density = Mass ÷ Volume = 540 ÷ 60 = 9 g/cm³

Interpret

Since 9 > 1, this metal sinks in water.

Density = 9 g/cm³

📝 Example 6: Finding mass

Given

Density = 8 g/cm³. Volume = 25 cm³. Find the mass.

Calculate

Mass = Density × Volume = 8 × 25 = 200 g

Mass = 200 g

📝 Example 7: Finding volume

Given

Gold has a density of 19.3 g/cm³. A gold bar has mass 965 g. Find its volume.

Calculate

Volume = Mass ÷ Density = 965 ÷ 19.3 = 50 cm³

Volume = 50 cm³

Pressure

Pressure is a compound measure that relates the force applied to the area over which it acts. The greater the force on a smaller area, the higher the pressure.

Pressure = Force ÷ Area | Force = Pressure × Area | Area = Force ÷ Pressure

Units: Pascals (Pa) = N/m² (Newtons per square metre)

📝 Example 8: Finding pressure

Given

A force of 600 N acts on an area of 20 m². Find the pressure.

Calculate

Pressure = Force ÷ Area = 600 ÷ 20 = 30 Pa

Pressure = 30 Pa

📝 Example 8b: Finding area (rearranging the formula)

Given

A force of 360 N produces a pressure of 90 Pa. Find the area it is acting on.

Rearrange

We are given force and pressure but need area, so use: Area = Force ÷ Pressure

Calculate

Area = 360 ÷ 90 = 4 m²

Area = 4 m²

📝 Example 8c: Finding force (rearranging the formula)

Given

A pressure of 50 Pa acts over an area of 4 m². Find the force.

Rearrange

We are given pressure and area but need force, so use: Force = Pressure × Area

Calculate

Force = 50 × 4 = 200 N

Force = 200 N

💡 Real life: High-heeled shoes exert much more pressure than flat shoes because the same force (body weight) is concentrated on a tiny area (the heel tip). Snow shoes work by spreading force over a large area to reduce pressure.

✓ Quick Check 2 — Density, Pressure & Real-Life Contexts

Question 1 of 10

Converting Units in Compound Measures

When working with speed, you often need to convert between m/s and km/h. This requires understanding that both the distance unit and the time unit change at once.

m/s → km/h: multiply by 3.6 | km/h → m/s: divide by 3.6

📝 Example 9: Convert 15 m/s to km/h

Calculate

15 × 3.6 = 54 km/h

15 m/s = 54 km/h

📝 Example 10: Convert 90 km/h to m/s

Calculate

90 ÷ 3.6 = 25 m/s

90 km/h = 25 m/s

Compound measure	Formula	Units	Rearrangements
Speed	S = D ÷ T	mph, km/h, m/s	D = S×T T = D÷S
Density	D = M ÷ V	g/cm³, kg/m³	M = D×V V = M÷D
Pressure	P = F ÷ A	Pa (N/m²)	F = P×A A = F÷P

SDT Calculator — enter any two values to find the third

Leave ONE box empty. The calculator will work out the missing value.

Speed (km/h)

Distance (km)

Time (hours)

✓ Quick Check 3 — Finding Distance, Time & Unit Conversions

Question 1 of 10

Practice: Compound Measures

Enter your answers as numbers.

#	Question	Answer	Result
1	A car travels 150 km in 3 hours. What is its speed (km/h)?
2	A car travels at 60 km/h for 2.5 hours. What distance does it cover (km)?
3	A car travels 200 km at 40 km/h. How long does the journey take (hours)?
4	A block has mass 50g and volume 10cm³. What is its density (g/cm³)?
5	A force of 100N acts on an area of 4m². What is the pressure (N/m²)?
6	A cyclist travels 45 km in 3 hours. What is their speed (km/h)?
7	A train travels at 80 km/h for 1.5 hours. What distance does it cover (km)?
8	A runner covers 21 km at 7 km/h. How long does it take (hours)?
9	A metal block has mass 120g and volume 15cm³. What is its density (g/cm³)?
10	A force of 250N acts on an area of 5m². What is the pressure (N/m²)?

⚠ Things to Watch Out For

For speed, use Speed = Distance ÷ Time — don't accidentally divide distance by speed to get time.
Time must be in hours when using speed in km/h or mph — convert minutes to a decimal fraction of an hour first.
For density, Density = Mass ÷ Volume — don't confuse which quantity goes on top.
For pressure, Pressure = Force ÷ Area — larger area means lower pressure, not higher.
Keep units consistent throughout — don't mix km and m, or g and kg, in the same calculation.

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SDT Calculator — enter any two values to find the third

Practice: Compound Measures

⚠ Things to Watch Out For