Speed, Distance & Time

Grade 4

What speed actually is

Speed is a compound measure — it's made by combining two other quantities (distance and time). It tells you how much distance is covered in one unit of time.

The three quantities are locked together by one formula:

Speed = Distance ÷ Time

Rearranged: Distance = Speed × Time, and Time = Distance ÷ Speed.

The triangle — cover-up method

Draw a triangle with D at the top, and S × T at the bottom. To find any quantity, cover it up and read what's left:

Cover D: Distance = Speed × Time. Cover S: Speed = Distance ÷ Time. Cover T: Time = Distance ÷ Speed.

The triangle is a memory aid, not a method. Make sure you understand why each version works — examiners sometimes phrase questions in ways that catch out triangle-only learners.

Worked example

EXAMPLE

A car travels 150 km in 2.5 hours. What is its average speed?

Speed = Distance ÷ Time = 150 ÷ 2.5 =60 km/h.

Units — the most common mistake

Always check your units match before calculating. If the distance is in km and the time is in minutes, convert first. Speed in km/h needs distance in km and time in hours. Mixing units is the single biggest source of errors in compound measure questions.

EXAMPLE

A cyclist covers 24 km in 40 minutes. Find the speed in km/h.

Convert time to hours: 40 ÷ 60 = 2/3 hours. Speed = 24 ÷ (2/3) = 24 × 3/2 =36 km/h.

Try this one

A train travels at 90 km/h for 40 minutes, then at 60 km/h for 30 minutes.

(a) Find the total distance the train travels. [2]

(b) A car travels the same total distance in 1 hour 15 minutes. Find the average speed of the car in km/h. [2]

Nova's hint:

This uses speed, distance, time with unit conversion.

Ask yourself: 'Have I converted the times into hours before using Distance = Speed × Time?' For example, 20 minutes = 20/60 = 1/3 of an hour.

Try to Solve it with Nova?