 Applications of rates

Lesson

A rate is a ratio between two measurements with different units. A common example of a rate is speed (which is written in kilometres per hour or km/h). You can see that this describes a relationship between two measurements- kilometres and hours.

In fact, we use rates all the time in every life and they can be really useful. For example, we use rates to calculate how much money you earn in a week, how far you can go on a tank of gas or how many cars a company can make per hour.

Let's look through some more examples to see rates in action in everyday life.

Worked Examples

Christa earns $\$21$$21 per hour working as a receptionist. If she works 1919 hours per week, how much is her weekly wage? Question 2 Maria is a web designer who runs her own business. She charges an hourly rate of \136$$136.

1. On call outs between 5pm and 11pm, Maria charges a time and a half rate. What is her hourly rate for callouts between 5pm and 11pm?

2. On urgent jobs requiring her to work on weekends and public holidays Maria charges a double time rate. What is her hourly rate for callouts on weekends and public holidays?

Question 3

Luke is a locksmith. On weekends, if he is on call, he gets paid $\$64.50$$64.50 per hour plus a flat rate call out fee of \75$$75.

On the coming Saturday he has $3$3 jobs that will take $1.5$1.5, $0.25$0.25 and $1.25$1.25 hours respectively to complete. How much will he earn on Saturday?

Outcomes

9P.NA1.05

Solve problems involving ratios, rates, and directly proportional relationships in various contexts (e.g., currency conversions, scale drawings, measurement), using a variety of methods (e.g., using algebraic 15 20 x 4 reasoning, equivalent ratios, a constant of proportionality; using dynamic geometry software to construct and measure scale drawings)