Mathematics Standard • Year 11 • Module 3 • Lesson 2
Overtime, Penalty Rates and Allowances
Build fluency in penalty-rate multipliers, mixed overtime calculations, and adding allowances correctly.
1. Quick recall
Answer each question in the space provided. 1 mark each
Q1.1 Write the multiplier used for each penalty rate:
Time-and-a-half = × ____ Double time = × ____ Double time and a half = × ____
Q1.2 True or false: a $15/day meal allowance becomes $22.50/day on a time-and-a-half overtime day. Circle T / F and explain in one sentence.
Q1.3 Complete the formula for gross pay including overtime and allowances:
Gross pay = ______________ + ______________ + ______________
2. Worked example — total pay with overtime + allowance
Follow each line. Every step has a reason on the right.
Problem. Tom earns $22.80/hr. This week he works 38 ordinary hours, plus 5 hours of overtime at time-and-a-half, plus he receives a $48 weekly travel allowance. Calculate his weekly gross pay.
Step 1 — Calculate the overtime rate first.
rOT = $22.80 × 1.5 = $34.20/hr
Reason: multiply the base rate by 1.5 once, then use it for any number of overtime hours.
Step 2 — Ordinary pay.
Ordinary = $22.80 × 38 = $866.40
Step 3 — Overtime pay.
Overtime = $34.20 × 5 = $171.00
Step 4 — Add the allowance (do not multiply it).
Allowance = $48.00 (flat weekly amount)
Reason: allowances are NOT subject to overtime multipliers.
Step 5 — Sum every component.
Gross = $866.40 + $171.00 + $48.00 = $1,085.40
Conclusion. Weekly gross pay = $1,085.40.
3. Faded example — Saturday + Sunday penalty rates
Alinta earns $18.60/hr. Last week she worked 38 ordinary hours, 3 hours on Saturday at time-and-a-half, and 4 hours on Sunday at double time. Calculate her total weekly pay. Fill in each blank. 4 marks
Step 1 — Calculate each rate first:
Saturday rate rSat = $18.60 × ____ = $ ____________ /hr
Sunday rate rSun = $18.60 × ____ = $ ____________ /hr
Step 2 — Ordinary pay:
Ordinary = $18.60 × 38 = $ ____________
Step 3 — Saturday + Sunday pay:
Saturday = $ __________ × 3 = $ ____________
Sunday = $ __________ × 4 = $ ____________
Step 4 — Sum:
Total = $ __________ + $ __________ + $ __________ = $ ____________
4. Graduated practice — overtime, penalty rates and allowances
Show your working in the space below each part. Keep dollar amounts to 2 decimal places.
Foundation — calculate the penalty rate (4 questions)
| Q | Problem | Answer |
|---|---|---|
| 4.1 1 | Base rate $20.00/hr. What is the time-and-a-half rate? | |
| 4.2 1 | Base rate $26.40/hr. What is the double-time rate? | |
| 4.3 1 | Base rate $31.50/hr. What is the double-time-and-a-half rate? | |
| 4.4 1 | Base rate $24.80/hr. Calculate the pay for 6 hours at time-and-a-half. |
Standard — typical HSC difficulty (6 questions)
Show at least one line of substitution and clearly label your final answer with units.
4.5 Nina earns $28.60/hr. She works 38 ordinary hours plus 4 hours at time-and-a-half. Calculate her total weekly pay. 2 marks
4.6 A worker earns $24.80/hr. On Saturday she works 6 hours at time-and-a-half and also receives a $18 travel allowance for the day. Calculate the total Saturday pay. 2 marks
4.7 An employee earns $32.00/hr. They work 38 ordinary hours, 2 hours at time-and-a-half, and 3 hours at double time. Calculate the total weekly pay. 2 marks
4.8 Jade is a plumber earning $29.50/hr for 38 ordinary hours and a tool allowance of $16.80 per day over 5 working days. Calculate her gross weekly pay. 2 marks
4.9 An employee's base rate is $31.50/hr. Calculate her pay rate per hour for a public holiday paid at double time and a half. 1 mark
4.10 A tradesperson works 4 days, 8 hours per day at $27.00/hr plus a $22.50/day meal allowance. Calculate the total gross pay over the 4 days. 2 marks
Extension — tiered overtime + allowance (2 questions)
4.11 A worker earns $25.40/hr. In one week, they work 38 ordinary hours, the first 2 overtime hours at time-and-a-half, and the next 3 overtime hours at double time. Calculate the total gross pay. 3 marks
4.12 A nurse earns $34.80/hr. In one fortnight she works 76 ordinary hours, 5 hours at time-and-a-half, 4 hours at double time, and receives a $32.50 first-aid allowance per week. Calculate her fortnightly gross pay. 3 marks
5. Self-check the easy 3
Tick the first three once you've checked your method works.
How did this worksheet feel?
What I'll revisit before next class:
Q1.1 — Penalty multipliers
Time-and-a-half = × 1.5. Double time = × 2.0. Double time and a half = × 2.5.
Q1.2 — Allowance on a penalty day
FALSE. Allowances are not subject to penalty multipliers — a $15/day meal allowance stays $15/day on a time-and-a-half day. Only the base hourly rate changes.
Q1.3 — Gross pay formula
Gross pay = Ordinary pay + Overtime pay + Allowances.
Q3 — Faded example (Saturday + Sunday)
Step 1: rSat = $18.60 × 1.5 = $27.90/hr. rSun = $18.60 × 2.0 = $37.20/hr.
Step 2: Ordinary = $18.60 × 38 = $706.80.
Step 3: Saturday = $27.90 × 3 = $83.70. Sunday = $37.20 × 4 = $148.80.
Step 4: Total = $706.80 + $83.70 + $148.80 = $939.30.
Q4.1 — Time-and-a-half from $20.00
$20.00 × 1.5 = $30.00/hr.
Q4.2 — Double time from $26.40
$26.40 × 2 = $52.80/hr.
Q4.3 — Double time and a half from $31.50
$31.50 × 2.5 = $78.75/hr.
Q4.4 — 6 hours at time-and-a-half
OT rate = $24.80 × 1.5 = $37.20/hr. Pay = $37.20 × 6 = $223.20.
Q4.5 — Nina's weekly pay
OT rate = $28.60 × 1.5 = $42.90/hr.
Ordinary = $28.60 × 38 = $1,086.80.
Overtime = $42.90 × 4 = $171.60.
Total = $1,258.40.
Q4.6 — Saturday pay + allowance
Sat rate = $24.80 × 1.5 = $37.20/hr.
Sat pay = $37.20 × 6 = $223.20.
With allowance = $223.20 + $18.00 = $241.20.
Q4.7 — Mixed overtime
Ordinary = $32.00 × 38 = $1,216.00.
Time-and-a-half rate = $32.00 × 1.5 = $48.00/hr → 2 hours = $96.00.
Double time rate = $32.00 × 2 = $64.00/hr → 3 hours = $192.00.
Total = $1,216 + $96 + $192 = $1,504.00.
Q4.8 — Plumber with tool allowance
Base = $29.50 × 38 = $1,121.00.
Tool allowance = $16.80 × 5 = $84.00.
Gross = $1,121.00 + $84.00 = $1,205.00.
Q4.9 — Double time and a half rate
$31.50 × 2.5 = $78.75/hr.
Q4.10 — Tradesperson 4 days
Hours pay = $27.00 × 32 = $864.00. Allowance = $22.50 × 4 = $90.00. Total = $954.00.
Q4.11 — Tiered overtime
Ordinary = $25.40 × 38 = $965.20.
First OT rate = $25.40 × 1.5 = $38.10/hr → 2 hours = $76.20.
Second OT rate = $25.40 × 2.0 = $50.80/hr → 3 hours = $152.40.
Gross = $965.20 + $76.20 + $152.40 = $1,193.80.
Q4.12 — Nurse fortnightly
Ordinary = $34.80 × 76 = $2,644.80.
Time-and-a-half rate = $34.80 × 1.5 = $52.20/hr → 5 hours = $261.00.
Double time rate = $34.80 × 2 = $69.60/hr → 4 hours = $278.40.
Allowance for fortnight = $32.50 × 2 = $65.00.
Fortnightly gross = $2,644.80 + $261.00 + $278.40 + $65.00 = $3,249.20. (Common slip: only adding one week of allowance.)