Speed, Distance and Time

What you will learn

• Use $v = d \div t$ and rearrange it.
• Match units of distance, time and speed.
• Find average speed for a journey with several parts.

Before you start: you should know how to divide decimals and how to change minutes into hours. See Unit Conversions and Elapsed Time and Timetables.

The idea

Speed tells you how far something goes in a given time. If a car travels $120$ km in $2$ hours, its speed is $120 \div 2 = 60$ km/h, read “kilometres per hour”.

$v = \frac{d}{t}$

Rearranged, $d = v \times t$ gives the distance, and $t = d \div v$ gives the time.

Units must match

Speed in km/h needs distance in km and time in hours. If the time is in minutes, change it first: $30$ minutes is $0.5$ hours, and $15$ minutes is $0.25$ hours. To change m/s to km/h, multiply by $3.6$. To change km/h to m/s, divide by $3.6$.

Average speed

The average speed for a whole journey is the total distance divided by the total time. It is not the average of the speeds, unless the times are equal.

Worked examples

Example 1: Finding speed

A runner covers $10$ km in $50$ minutes. Find the speed in km/h.

1. $50$ minutes is $50 \div 60 = \tfrac{5}{6}$ hours.
2. $10 \div \tfrac{5}{6} = 10 \times \tfrac{6}{5} = 12$.

Answer: $12$ km/h

Example 2: Finding time

A plane flies $900$ km at $600$ km/h. How long does it take in hours and minutes?

1. $t = 900 \div 600 = 1.5$ hours.
2. $0.5$ hours is $30$ minutes.

Answer: $1$ hour $30$ minutes

Example 3: Average speed

A cyclist rides $20$ km at $10$ km/h, then $20$ km at $20$ km/h. Find the average speed.

1. First part: $20 \div 10 = 2$ hours. Second part: $20 \div 20 = 1$ hour.
2. Total distance $40$ km, total time $3$ hours.
3. $40 \div 3 \approx 13.3$.

Answer: about $13.3$ km/h, not $15$ km/h.

Tip: cover the quantity you want in the formula triangle: speed over distance and time. What is left tells you whether to divide or multiply.

Why it matters

Speed, distance and time connect to journey planning, sport, speed limits and science. Pilots, drivers and runners all use the formula to plan arrival times and fuel, and it is the first example of a rate, a quantity that compares two different units.