Rates

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.

Question 2

Question: If Charlie earns $14 per hour and he works for $17$17 hours, how much money does he earn?

Think: Charlie's rate of pay (R) could be expressed as dollars/hour. We could write this as:

$\text{Rate of Pay}=\frac{\text{Total Amount Earned}}{\text{Total Hours Worked}}$Rate of Pay=Total Amount EarnedTotal Hours Worked​

So to calculate the total amount Charlie earned, we would calculate Rate of pay x Total Hours worked.

Do: $14\times17$14×17 = $\$238$$238

Charlie earned $\$238$$238.

 

Question 3

 

Converting rates

We can also change the units of measurement that our rates are expressed in. For example kilometres/hour can be changed to metres/second. We just need to be aware of how the values are changing when we are converting the quantities as we need to keep our rate in the same proportion. 

Examples

Question 4

Convert: $13$13 L/hr to L/day.

Think: How are our units of measurement are changing. We only need to change one of our units of measurement- that is, we need to change hours to days. Since there are $24$24 hours in a day, we need  to multiply both sides of our rate by $24$24.

Do:

$13$13 L/hr	$=$=	$312$312 L/ 24 hrs	multiply by 24 to get 24hrs
	$=$=	$312$312 L/day

We may need to change both units of measurement in some questions.

 

Question 5

 

This type of conversion is also useful when we look at exchange rates. 

Question 6

 

Question 7