Speed, Distance, and Time: KS3 Maths Formulae and Worked Examples

Speed, distance, and time are connected by three simple formulae that appear in almost every KS3 maths exam. Knowing how to rearrange and apply them — and how to handle different units — allows you to solve a wide range of real-world problems from journey planning to science investigations.

What are the three speed, distance, and time formulae?

The three quantities are linked by a single relationship. Rearranging it gives three formulae, one for each unknown:

These three are really one formula written in different ways. If you know any two of the three quantities, you can always find the third.

How do I use the formula triangle?

The SDT triangle (sometimes called the DST triangle) is a memory aid. Draw a triangle and write D at the top, S at the bottom-left, and T at the bottom-right:

    D
  -----
  S | T

To find any quantity, cover it with your finger. What remains shows the formula:

• Cover D: S and T are side by side → D = S × T
• Cover S: D is above T → S = D ÷ T
• Cover T: D is above S → T = D ÷ S

The triangle is a helpful reminder, but you do not have to draw it in an exam — the formulae in the table above are equally valid written from memory.

How do I handle different units of measurement?

Units must be consistent before you apply any formula. Speed, distance, and time each have a unit, and they must be compatible:

• If speed is in km/h, time must be in hours and distance will be in km.
• If speed is in m/s, time must be in seconds and distance will be in metres.

Converting time: minutes to hours

Divide by 60. For example, 20 minutes = 20 ÷ 60 = 1/3 hour.

Converting between km/h and m/s

• km/h → m/s: divide by 3.6 (because 1 km/h = 1000 ÷ 3600 m/s)
• m/s → km/h: multiply by 3.6

Worked Example — Convert 90 km/h to m/s

90 ÷ 3.6 = 25 m/s

Check: 25 m/s × 3600 s = 90 000 m = 90 km ✓

Always check that your final answer has a sensible unit and a sensible magnitude — a speed of 50 000 km/h for a car would be a clear sign something has gone wrong.

How do I calculate average speed?

Average speed = total distance ÷ total time

This is not the same as the average of the individual speeds. You must add all the distances together and divide by the total time taken, not average the speed values.

Worked Example — Average speed over a journey in two stages

A car travels 60 km at 40 km/h, then a further 90 km at 60 km/h. Find the average speed for the whole journey.

• Time for stage 1: T = D ÷ S = 60 ÷ 40 = 1.5 hours
• Time for stage 2: T = D ÷ S = 90 ÷ 60 = 1.5 hours
• Total distance: 60 + 90 = 150 km
• Total time: 1.5 + 1.5 = 3 hours
• Average speed: 150 ÷ 3 = 50 km/h

Note: (40 + 60) ÷ 2 = 50 km/h gives the same numerical answer here, but only by coincidence (because the two stages happen to take equal time). The correct method is always total distance ÷ total time.

Can you show me some step-by-step worked examples?

Worked Example 1 — Find speed

A cyclist travels 150 km in 3 hours. What is her speed?

S = D ÷ T = 150 ÷ 3 = 50 km/h ✓

Worked Example 2 — Find distance

A lorry travels at 60 mph for 2.5 hours. How far does it travel?

D = S × T = 60 × 2.5 = 150 miles ✓

Worked Example 3 — Find time

A train travels 240 km at an average speed of 80 km/h. How long does the journey take?

T = D ÷ S = 240 ÷ 80 = 3 hours ✓

Worked Example 4 — Unit conversion required

A car travels at 45 km/h for 20 minutes. How far does it travel?

Convert time: 20 minutes = 20 ÷ 60 = 1/3 hour.

D = S × T = 45 × (1/3) = 15 km ✓

Worked Example 5 — Multi-stage journey

Already shown in the average speed section above: the answer is 50 km/h.

What are the most common mistakes in speed, distance, and time problems?

Being aware of these pitfalls will save marks.

Mistake 1 — Mixing units

Using speed in km/h with time in minutes without converting is the single most common error. Always convert time to hours when speed is in km/h, or to seconds when speed is in m/s.

Mistake 2 — Averaging the speeds

Students often add the two speeds and divide by 2 to find average speed. This only gives the correct answer if the two stages take equal time, which is rarely stated. Always use total distance ÷ total time.

Mistake 3 — Applying the wrong formula

Writing S = D × T instead of S = D ÷ T is very common. Using the formula triangle to double-check avoids this. If you cover S, you see D above T — that means divide, not multiply.

Mistake 4 — Leaving time in decimal form without interpreting it correctly

A time of 2.5 hours means 2 hours 30 minutes, not 2 hours 5 minutes. Be careful when converting decimals back into hours and minutes: the decimal part represents a fraction of an hour, so multiply it by 60 to find the minutes (0.5 × 60 = 30 minutes).

Frequently Asked Questions

Does it matter which formula I use first?

No — rearrange the single relationship S = D ÷ T (or equivalently D = S × T) to suit whichever quantity is unknown. The formula triangle helps you pick the right rearrangement instantly. If you write down all three formulae at the top of your working and circle the one you need, you are less likely to use the wrong one under exam pressure.

How do I convert between mph and km/h?

The conversion factor is approximately 1 mile ≈ 1.609 km, so 1 mph ≈ 1.609 km/h. To convert mph to km/h multiply by 1.609; to convert km/h to mph divide by 1.609 (or multiply by 0.621). At KS3 you will usually be given this conversion factor in the question if it is needed.

What if the journey has more than two stages?

The method is the same: add all the individual distances to get total distance, add all the individual times to get total time, then divide. With three or more stages you simply have more rows to sum before applying average speed = total distance ÷ total time.

Can speed be negative?

In KS3 maths, speed is always taken as a positive quantity representing how fast something is moving. Direction is not considered at this level. Velocity (which can be negative, representing movement in the opposite direction) is introduced later in GCSE physics and higher maths.

Ask Professor Pi a speed, distance, and time question right now at aitutors.me — and get a Socratic hint rather than just the answer, so the method sticks.