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$$21 per hour working as a receptionist. If she works $19$19 hours per week, how much is her weekly wage?
Question 2
Sally can vacuum $3$3 rugs in $15$15 minutes and squeeze $6$6 oranges in $24$24 minutes.
How long does it take to vacuum $1$1 rug?
How long does it take to squeeze $1$1 orange?
How long would it take for Sally to vacuum $8$8 rugs and squeeze $12$12 oranges?
Question 3
Luke is a locksmith. On weekends, if he is on call, he gets paid $\$64.50$$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.
 |
Calculate the cost of a call with a duration of $6$6 minutes and $19$19 seconds on a $19 plan with Vodafone.
Calculate the cost of a call with a duration of $6$6 minutes and $19$19 seconds on a $19 plan with Optus.
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.
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.
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
ATelstra
BVirgin
CVodafone
D