Speed, Distance & Time

Spec reference: Ratio, proportion and rates of change
Key idea: Use the relationship between speed, distance and time to solve problems.

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▶ Conversion Graphs

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The formula triangle

$$\text{Speed}=\frac{\text{Distance}}{\text{Time}}\text{Distance}=\text{Speed}\times \text{Time}\text{Time}=\frac{\text{Distance}}{\text{Speed}}$$

Cover the quantity you want to find:

$$\boxed{{\displaystyle \frac{D}{S\times T}}}$$

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Units

Speed	Distance	Time
m/s	metres	seconds
km/h	kilometres	hours
mph	miles	hours

WARNING

Always make sure units are consistent before calculating.

Convert minutes to hours: divide by 60.
Convert hours to minutes: multiply by 60.

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Worked examples

Example

A car travels 240 km in 3 hours. Find the average speed.

$$\text{Speed}=\frac{240}{3}=\boxed{{\displaystyle 80\text{ km/h}}}$$

Example

A cyclist travels at 15 mph for 2.5 hours. Find the distance.

$$\text{Distance}=15\times 2.5=\boxed{{\displaystyle 37.5\text{ miles}}}$$

Example

A train travels 180 km at 90 km/h. How long does the journey take?

$$\text{Time}=\frac{180}{90}=2\text{ hours}$$

Answer: $\boxed{{\displaystyle 2\text{ hours}}}$

Example

A journey of 45 km takes 36 minutes. Find the average speed in km/h.

Convert 36 minutes to hours: $36÷60=0.6$ hours

$$\text{Speed}=\frac{45}{0.6}=\boxed{{\displaystyle 75\text{ km/h}}}$$

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Distance-time graphs

• Gradient = speed
• Horizontal line = stationary (not moving)
• Steeper line = faster speed
• Negative gradient = returning to start

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Exam tips

Watch out for

• Always convert time to hours (not minutes) when speed is in km/h or mph
• Average speed = total distance ÷ total time (not the mean of the speeds)

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Test Yourself

Question 1 of 5

300 km in 4 hours. Average speed?