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← Back to Commercial Maths & Proportion
1Percentage2Unitary Method3Percentage of a Quantity4Ratio & Proportion5Speed, Distance & Time6Simple Interest7Counting Principle

Concept 5 of 7

Speed, Distance & Time

1

Today's big idea

Knowing any two of distance, speed and time gives the third, if the units match.

Average speed is total distance over total time, never the mean of two speeds.

2

How it works

👀 What's going on?

A train timetable, a car's dashboard and a running app all juggle the same three numbers. Knowing any two of them pins the third exactly.

💡 Here's the trick

One hour, one jump. Speed is the size of the jump.kmhours0080116022403+80+80+803 hours is 3 jumps of 80 km, so distance is 240 km.One picture answers all three: jump size, jumps taken, distance reached.

Look at the lines above. The two scales run locked together, so every hour on one is a fixed jump along the other. That lock is what lets any two of the three quantities give you the third.

🪄 How to do it

  1. 1.Read the pairing off the lines above.
  2. 2.Check both quantities are in matching units before anything else.
  3. 3.Divide to find a rate, or multiply to extend one.

✍️ Try it

A bus covers 210 km in 3 hours; what is its speed? Then: how long does a 45 km trip take at 30 km per hour?

Speed is 210 divided by 3, which is 70 km per hour. Time is 45 divided by 30, giving 1.5 hours, or 1 hour 30 minutes.

⚠️ Watch out

You might be thinking average speed over two legs is the average of the two speeds. It is not. Average speed is the whole distance divided by the whole time, and the slower leg takes longer, so it counts for more.

🌟 Why this matters

Working out when to leave to arrive on time is this calculation, and so is judging whether a journey estimate is realistic.
Exam tip: Convert minutes to hours before you divide, since mixed units cause most of the errors here.

3

Watch me solve one

Quanta solves it

“Watch how I think through one of these — then you try.”

THE PROBLEM

“A bus covers 210 km in 3 hours. Find its speed.”

  1. 1

    Recall formula

    S = D ÷ T. 🚗

  2. 2

    Substitute

    210 ÷ 3 = 70

  3. 3

    Answer ✓

    70 km/h

Now you try one — same steps, different story 👇

4

See it in action

⚡ Time to play!

Cover the unknown in the D / (S × T) triangle. What's left is the formula. Convert fractional time to a decimal.

SPEED · ROUND 1 OF 3

Given: Speed 50 km/h, Time 3 h. Find the Distance.

DS×T

Cover the Distance. Which formula is left?

5

Quick check

✅ VERIFICATION

A car drives 60 km at 60 km/h, then 60 km at 30 km/h. What is its average speed for the whole journey?

⚡ Finish the activity above first to answer.

Keep going!

Up next: Simple Interest

si = (P × R × T) ÷ 100. Per year.

Concept 6 of 7 →