Study Tips

Speed, Distance and Time: The Formula Triangle Explained

By Math Solving Space · · 2 min read

On this page
  1. The formula triangle
  2. Worked example 1: speed
  3. Worked example 2: time
  4. Hours and minutes
  5. Units
  6. Distance–time graphs
  7. Common mistakes
  8. Practice questions
  9. Frequently asked questions

Speed, distance and time are connected by one formula: speed = distance ÷ time. Rearranged, distance = speed × time and time = distance ÷ speed. The formula triangle helps you remember: cover what you want to find and the other two show the calculation.

The formula triangle

S=DTD=S×TT=DSS = \frac{D}{T} \qquad D = S \times T \qquad T = \frac{D}{S}

Picture DD on top, with SS and TT side by side underneath.

Worked example 1: speed

A car travels 150 km in 2.5 hours:

S=1502.5=60 km/hS = \frac{150}{2.5} = 60 \text{ km/h}

Worked example 2: time

How long does 210 km take at 70 km/h?

T=21070=3 hoursT = \frac{210}{70} = 3 \text{ hours}

Hours and minutes

Times in calculations must be decimal hours. 2 hours 15 minutes is 2+1560=2.252 + \frac{15}{60} = 2.25 hours, not 2.15.

Going back: 1.75 hours is 1 hour and 0.75×60=450.75 \times 60 = 45 minutes.

Units

Keep units consistent: km with km/h, miles with mph, metres with m/s. To convert, 100 km/h≈62.14 mph100 \text{ km/h} \approx 62.14 \text{ mph} and 1 m/s=3.6 km/h1 \text{ m/s} = 3.6 \text{ km/h}.

Distance–time graphs

Distance goes up, time across. A straight line means constant speed, and the slope is the speed. A flat section means the object has stopped.

Common mistakes

  • Using minutes with km/h without converting.
  • Averaging two speeds instead of using total distance ÷ total time.
  • Mixing km and miles.

Practice questions

  1. A cyclist rides 45 km in 1 h 30 min. Find the speed.
  2. How far do you go in 40 minutes at 90 km/h?
  3. Convert 20 m/s to km/h.

Answers: 1) 30 km/h 2) 60 km 3) 72 km/h

Use the speed, distance and time calculator for any of the three, the unit converter to change units, and the time calculator for clock times.

Frequently asked questions

What is average speed?

Total distance divided by total time, including any stops.

Why can't I average two speeds?

If you spend different amounts of time at each speed, a simple average gives the wrong answer. Always use total distance ÷ total time.

How do I convert km/h to m/s?

Divide by 3.6.

Open the calculator →

#everyday maths#speed

Related guides