Speed, Distance and Time: The Formula Triangle + Examples

Speed is the distance travelled divided by the time taken. These three quantities — speed, distance and time — are linked by one formula, and the whole topic is really just rearranging that formula. It is taught in Year 5 and returns in secondary physics.

The Formula Triangle

where v is speed, s is distance and t is time.

Picture a triangle with s on top and v and t below. Cover the quantity you want with a finger and what remains is the formula:

One triangle replaces three memorised formulas. A child who memorises three separate formulas will mix them up; a child who draws the triangle never does.

Units of Speed

Speed is always a distance unit per time unit: km/h, m/s or m/min. The unit must match the distance and time used. If distance is in km and time in hours, the speed is in km/h.

Converting km/h to m/s

This is where most errors happen, and there is only one number to know:

• km/h → m/s: divide by 3.6
• m/s → km/h: multiply by 3.6

The 3.6 comes from 1,000 metres divided by 3,600 seconds. Explaining where the number comes from is more useful than asking a child to memorise it, because they can then rebuild it whenever they forget.

Example: 72 km/h = 72 ÷ 3.6 = 20 m/s

Basic Worked Examples

A car covers 240 km in 3 hours. What is its speed?

v = 240 ÷ 3 = 80 km/h

A motorbike travels at 60 km/h for 2.5 hours. How far does it go?

s = 60 × 2.5 = 150 km

Meeting and Catch-Up Problems

These two forms are the most feared, yet both turn on a single idea.

Meeting — two vehicles set off from different places towards each other. Their speeds are added, because the gap closes from both ends at once.

A and B are 300 km apart. A car leaves A at 60 km/h and another leaves B at 40 km/h at the same moment. When do they meet?

t = 300 ÷ (60 + 40) = 3 hours

Catching up — both travel the same way and the one behind is chasing. Their speeds are subtracted, because only the difference matters.

A motorbike leaves at 08:00 at 40 km/h. A car leaves at 09:00 at 60 km/h. When does the car catch up?

When the car sets off the bike is already 40 km ahead. The speed difference is 20 km/h.

t = 40 ÷ 20 = 2 hours after 09:00, so 11:00.

The Mistakes That Actually Cost Marks

1. Not converting time units. Writing 1 hour 30 minutes as 1.30 when it should be 1.5 hours. This is the number one cause, and it is rooted in fractions, not in speed. Half an hour is 0.5 hours, not 0.30.

2. Dividing the wrong way. Writing t = v ÷ s. The formula triangle removes this risk entirely.

3. Converting the wrong way with 3.6. Sanity-check it: 72 km/h and 20 m/s are the same speed, so if a conversion makes the number bigger, the direction is wrong.

4. Adding speeds in a catch-up problem. Meeting adds, catching up subtracts. A memory hook: approaching each other, both are working; travelling the same way, only the difference works.

5. Forgetting the head start in catch-up problems. If the chaser leaves an hour later, that initial gap has to be worked out first.