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11.07 Using rates

Lesson

As rates arise frequently in everyday life, there are many practical uses for rates and calculations involving rates. 

For example, we can use a pay rate (dollars per hour) to calculate how much money is earned in a week; we can use the speed (km/h) to predict how long it would take to reach a given location; and we can use rates to calculate and compare the cost of different phone plans with differing charge rates for data ($/GB) and phone calls ($/min).

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

 

Worked example

If Steve earns $\$157.05$$157.05 for working $9$9 hours over the weekend and Tina earns $\$144.00$$144.00 for working $8$8 hours.

(a) Who has the better rate of pay?

Think: To work this out, we need a common point of comparison, let's work out how much each person earns per hour.

Do:

Steve: $\$157.05\div9$$157.05÷​9 hrs $=$= $\$17.45$$17.45/hr
       
Tina: $\$144.00\div8$$144.00÷​8 hrs $=$= $\$18.00$$18.00/hr

So now we can say with certainty that Tina's rate of pay is higher.

(b) How much will Tina earn in a week where she worked $35$35 hours at the same pay rate?

Think: She will receive $\$18$$18 for each hour she works. We need to multiply the pay rate by the number of hours.

Do:

Weekly pay $=$= $\$18\times35$$18×35
  $=$= $\$630$$630

 

(c) How many hours would Tina take to earn $\$1530$$1530?

Think: To find the number of hours we need to divide the total pay by the pay rate.

Do:

Hours worked $=$= $\frac{1530}{18}$153018
  $=$= $85$85 hours

 

Practice questions

Question 1

Christa earns $\$21$$21 per hour working as a receptionist. If she works $19$19 hours per week, how much is her weekly wage?

Question 2

Sally can vacuum $3$3 rugs in $15$15 minutes and squeeze $6$6 oranges in $24$24 minutes.

  1. How long does it take to vacuum $1$1 rug?

  2. How long does it take to squeeze $1$1 orange?

  3. How long would it take for Sally to vacuum $8$8 rugs and squeeze $12$12 oranges?

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?

Question 4

Consider the following phone plans.

  1. Calculate the cost of a call with a duration of $6$6 minutes and $19$19 seconds on a $19 plan with Vodafone.

  2. Calculate the cost of a call with a duration of $6$6 minutes and $19$19 seconds on a $19 plan with Optus.

  3. Calculate the cost of a call (in dollars) with a duration of $6$6 minutes and $19$19 seconds on a $20 plan with Telstra.

  4. Calculate the cost of a call (in dollars) with a duration of $6$6 minutes and $19$19 seconds on a $19 plan with Virgin.

  5. Suppose the included value of each plan has been used up for the month. Which plan would then be the most cost-effective for calls with durations of $6$6 minutes and $19$19 seconds?

    Optus

    A

    Telstra

    B

    Virgin

    C

    Vodafone

    D

Outcomes

2.3.10

complete calculations with rates, including solving problems involving direct proportion in terms of rate

2.3.11

use rates to make comparisons

2.3.12

use rates to determine costs

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