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Maths

Distance, speed and time

How far, how fast and how long are linked by one simple triangle. Learn the three formulas, keep your units the same, and journey questions become easy marks.

  • Ages 9 to 11
  • 11+ Maths
  • Worked examples

What is it?

Speed tells you how far something travels in one unit of time. A car going at 60 kilometres per hour (60 km/h) travels 60 km in each hour. Speeds can also be in miles per hour (mph) or metres per second (m/s).

If you know two of distance, speed and time, you can always work out the third: speed = distance ÷ time, distance = speed × time, and time = distance ÷ speed.

A typical question

A train travels 240 miles at 80 mph. How long does the journey take?

Triangle with D at the top, S and T at the bottomDST

Cover the letter you want. Cover D and you see S × T. Cover S and you see D over T (D ÷ T). Cover T and you see D over S (D ÷ S).

How to spot it

  • Words like 'how fast', 'average speed', 'how far' and 'how long does the journey take'.
  • Units with 'per': km/h, mph (miles per hour), m/s (metres per second).
  • Timetables or start and finish times, where you need the time taken first.
  • Journeys in two parts ('then it travelled…') asking for the average speed for the whole trip.

Step-by-step method

  1. Step 1: Write down what you know: D = ?, S = ?, T = ?, with units.
  2. Step 2: Pick the formula from the triangle: S = D ÷ T, D = S × T or T = D ÷ S.
  3. Step 3: Make the units match. If the speed is in km per hour, the time must be in hours: 30 minutes = 0.5 hours, 15 minutes = 0.25 hours, 20 minutes = ⅓ hour, 45 minutes = 0.75 hours.
  4. Step 4: Do the calculation.
  5. Step 5: Write the answer with its unit (km, mph, hours, minutes).
  6. Step 6: Check it makes sense: a person walking at 50 km/h, or a car taking 3 days to drive 100 miles, means something has gone wrong.

Worked examples

Example 1: finding the speed

Question: A car travels 120 km in 2 hours. What is its average speed?
  1. Step 1: D = 120 km, T = 2 hours, S = ?
  2. Step 2: S = D ÷ T = 120 ÷ 2 = 60.
  3. Step 3: The speed is 60 km/h.

Answer: 60 km/h

Example 2: finding the time

Question: A train travels 240 miles at 80 mph. How long does the journey take?
  1. Step 1: D = 240 miles, S = 80 mph, T = ?
  2. Step 2: T = D ÷ S = 240 ÷ 80 = 3.
  3. Step 3: The journey takes 3 hours.

Answer: 3 hours

Example 3: a time in minutes

Question: Amir walks at 6 km/h for 30 minutes. How far does he walk?
  1. Step 1: The speed is per hour, so change the time to hours: 30 minutes = 0.5 hours.
  2. Step 2: D = S × T = 6 × 0.5 = 3.
  3. Step 3: Or think: in a whole hour he walks 6 km, so in half an hour he walks half of that, 3 km.

Answer: 3 km

Example 4: an answer in minutes

Question: A bus travels 45 km at 60 km/h. How many minutes does it take?
  1. Step 1: T = D ÷ S = 45 ÷ 60 = 0.75 hours.
  2. Step 2: 0.75 hours = ¾ of 60 minutes = 45 minutes.
  3. Step 3: Quick check: 60 km/h is 1 km every minute, so 45 km takes 45 minutes.

Answer: 45 minutes

Example 5: average speed for a whole journey

Question: Mia cycles 60 km at 30 km/h, then 60 km at 60 km/h. What is her average speed for the whole journey?
  1. Step 1: First part: T = 60 ÷ 30 = 2 hours. Second part: T = 60 ÷ 60 = 1 hour.
  2. Step 2: Total distance = 60 + 60 = 120 km. Total time = 2 + 1 = 3 hours.
  3. Step 3: Average speed = total distance ÷ total time = 120 ÷ 3 = 40 km/h.
  4. Step 4: Not 45 km/h: she spends longer at the slower speed, so the average is nearer 30 than 60.

Answer: 40 km/h

Common traps

  • Mixing minutes and hours

    6 km/h for 30 minutes is not 6 × 30 = 180 km! Change minutes to hours first (30 minutes = 0.5 hours), or think in fractions of an hour.

  • Writing 1 hour 30 minutes as 1.3 hours

    There are 60 minutes in an hour, not 100. 1 hour 30 minutes = 1.5 hours, and 1.25 hours = 1 hour 15 minutes.

  • Averaging the two speeds

    For a journey in two parts, don't add the speeds and halve them. Find the total distance and the total time, then divide.

  • Using the wrong formula

    Speed = distance ÷ time, not time ÷ distance. Draw the triangle and cover the letter you want.

  • Leaving off the unit

    An answer of '3' could mean 3 hours or 3 minutes. Always write the unit.

Top tips

  • Draw the D/S×T triangle in the margin of your paper before you start.
  • Learn the handy times: 15 min = ¼ hour, 20 min = ⅓ hour, 30 min = ½ hour, 45 min = ¾ hour.
  • A speed of 60 km/h (or 60 mph) means 1 km (or 1 mile) every minute: a great shortcut.
  • For start and finish times, count on from the start time on a number line to find the time taken.
  • Average speed for a whole trip is always total distance ÷ total time.

Practice questions

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