Overtime and Extra Income II

People who earn wages are paid a set rate per hour to work a certain number of hours per week. If they work more than this set number of hours, they are entitled to receive overtime, which means that their rate of pay increases. This is done as an incentive to get people to work outside "normal" hours, such as on weekends or public holidays, or for working longer hours in one day than normal.

Common overtime rates

Time-and-a-half: payment to an employee at $1.5$1.5 times their usual hourly rate. 

Double time: payment to an employee at $2$2 times their usual hourly rate. 

Holiday loading

A holiday loading is a payment employees receive when they take paid annual leave. In Australia, the award rate is $17.5%$17.5% in addition to your regular rate of pay. So basically you're getting paid to take holidays- sounds awesome right?! 

There are a couple of reasons why holiday loadings were introduced

1. Since you generally spend more money when you are on holidays than when you are at work, holiday loadings help people with lower incomes afford to take holidays (especially since they are unable to earn overtime when they aren't working).
2. It encourages employees to take holidays. Theoretically, a person could "save up" all their annual leave and then take a year off which wouldn't be very helpful to a business who would have to pay the person who is away + someone to fill their role.

 

Examples

Question 1

Luke works as a private gardener and charges a normal hourly rate of $\$88$$88. However, time and a half applies to work on Saturdays and double time applies to work on Sundays.

Calculate the amount that Luke would charge for the following work:

A) $6$6 hours on a weekday

Think: Luke charges a normal rate on weekdays.

Do: $6\times88=\$528$6×88=$528

 

B) $7$7 hours on a Saturday

Think: Luke charges a time and a half rate on Saturdays.

Do: We could work out Luke's time and a half rate first then multiply it by the number of hours he works:

Time and a half rate: $88\times1.5=\$132$88×1.5=$132/ hour

Total charged: $132\times7=\$924$132×7=$924

Alternatively, we could do this all in one step:

$88\times1.5\times7=\$924$88×1.5×7=$924

 

C) $3.5$3.5 hours on a Sunday

Think: Luke charges a double time rate on Sundays. I am going to solve it in one step like I did in part B.

Do: $3.5\times88\times2=\$616$3.5×88×2=$616

 

D) $9$9 hours on a Friday, $8$8 hours on a Saturday and $9.5$9.5 hours on a Sunday

Think: This question combines all the different rates of pay- normal, time and a half and double.

Do: We can work them all out separately, then add the amounts together:

$9\times88$9×88	$=$=	$\$792$$792
$8\times88\times1.5$8×88×1.5	$=$=	$\$1056$$1056
$9.5\times88\times2$9.5×88×2	$=$=	$\$1672$$1672
$792+1056+1672$792+1056+1672	$=$=	$\$3520$$3520

We could also write all our working in one step which gives us the same answer:

$9\times88+8\times88\times1.5+9.5\times88\times2=\$3520$9×88+8×88×1.5+9.5×88×2=$3520

 

Question 2

Neil earns $\$910$$910. Calculate his normal hourly rate of pay, to the nearest cent, if he works:

$34$34 hours at normal rates and $10$10 hours at time-and-a-half

Think: How can we write an algebraic equation for this information?

Do:

$34x+10\times1.5x$34x+10×1.5x	$=$=	$910$910
$34x+15x$34x+15x	$=$=	$910$910
$49x$49x	$=$=	$910$910
$x$x	$=$=	$\frac{910}{49}$91049​
$x$x	$=$=	$18.571$18.571 ...

Neil's normal rate is $\$18.57$$18.57.

 

QUESTION 3