New Zealand
Level 6 - NCEA Level 1

# Rates II

Lesson

When we talk about speed limits, we often talk about them in terms of kilometres per hour. Think about what the expression km/h means. It is a rate that expresses a relationship between distance (kilometres) and time (hours). Speed is one of the most common rates that we see everyday. We can write this relationship as:

$SPEED=\frac{DISTANCE}{TIME}$SPEED=DISTANCETIME

In maths, we always like to write things in short hand, so we write this relationship as:

$S=\frac{D}{T}$S=DT

We can also rearrange this formula in a couple of ways:

$T=\frac{D}{S}$T=DS or $D=ST$D=ST

#### Examples

Let's look at how to use this formula in an example.

##### Question 1

Question: What is the speed of a car that travels $360$360km in $6$6 hours?

Do:

 $S$S $=$= $\frac{D}{T}$DT​ $=$= $\frac{360}{6}$3606​ $=$= $60$60 km/h

The speed of the car is $60$60km/h

This same process applies for all rates, not just speed.

### Outcomes

#### NA6-1

Apply direct and inverse relationships with linear proportions

#### 91026

Apply numeric reasoning in solving problems