Worksheet Grade 12 Math
Talbrook Water Authority Staffing: Operator Hours and Payroll
A grade 12 worksheet on staffing a fictional plant around the clock: coverage hours, full-time equivalents, overtime versus a new hire, and cost per connection.
Objectives
- Students will convert round-the-clock staffing requirements into full-time equivalent positions.
- Students will compare the cost of overtime coverage with the cost of an additional operator.
- Students will select the quantity that best supports a staffing decision and defend the choice.
Vocabulary
Key words: full-time equivalent, coverage hours, overtime rate, contact hour, licensure class, retirement-eligible
Teacher overview
A state permit that requires a licensed operator on duty at every hour sets a small utility's staffing floor, and the arithmetic of covering those hours decides how many people the utility must employ. The Bureau of Labor Statistics projects about 10,000 openings each year, on average, for water and wastewater treatment plant and system operators specifically, and EPA estimates that roughly one-third of the water sector workforce is eligible to retire within the next decade, so utilities like the fictional Talbrook Regional Water Authority in this worksheet plan coverage several years ahead. Students convert required coverage into full-time equivalents, then price two ways of closing the gap. The recurring error at this grade is dividing annual coverage hours by 2,080 rather than by the hours an operator is actually available after leave and training.
Student Worksheet
Every value below describes the fictional Talbrook Regional Water Authority. Talbrook runs one surface water plant that its state permit requires to have a licensed operator on duty every hour of every day. Talbrook serves 5,400 metered connections.
Staffing assumptions for this scenario:
- A full-time operator is paid for 40 hours per week across 52 weeks.
- Each operator takes 160 hours of paid leave and 80 hours of off-site training per year, and is not available to cover a shift during either.
- Overtime coverage is paid at $42.75 per hour.
- Talbrook budgets a new operator's salary at the national median of $60,020 per year, plus benefits equal to 32 percent of salary.
- In our scenario, Talbrook's state requires each licensed operator to complete 20 continuing-education contact hours every two years, and the approved course provider charges $95 per contact hour.
How many operator-hours of on-duty coverage does the plant need for one 365-day year?
How many hours per year is one full-time operator actually available to cover shifts, after leave and training are subtracted?
Using items 1 and 2, what is the smallest whole number of full-time operators that can cover the plant? Show the division and explain your rounding.
Talbrook currently employs 4 licensed operators. How many coverage hours per year are left uncovered by that staff?
Talbrook covers the item 4 hours with overtime at $42.75 per hour. What is the annual overtime cost?
Instead of overtime, Talbrook could hire a fifth operator. Find the full annual cost of that position, including benefits at 32 percent of the $60,020 salary.
How much more per year does the fifth operator cost than the overtime plan?
Talbrook budgets continuing education for a staff of 5 licensed operators. How many contact hours does the utility pay for in a single year?
At $95 per contact hour, what is Talbrook's annual continuing-education cost for those 5 operators?
Talbrook's operations department has 12 employees. If the department matches the national pattern of about one-third of the water workforce becoming retirement-eligible within a decade, how many positions is that?
Suppose Talbrook staffs the plant with 5 operators, each costing salary plus 32 percent benefits. What is the total annual operator payroll?
Divide your item 11 answer by Talbrook's 5,400 connections to find the annual operator payroll per connection. Round to the nearest cent.
Talbrook's board must decide whether to hire. Which quantity better supports that decision, the total payroll from item 11 or the payroll per connection from item 12? Defend your choice in two or three sentences.
Talbrook wants to fill the item 10 openings from its own community. Describe two different education paths a person could take into a licensed operator position, and state one advantage of each.
From Water for Schools (waterforschools.org). This material is in the public domain (CC0) and may be copied, edited, and shared freely.
Answer Key
Answer: 8,760 hours.
365 days x 24 hours per day = 8,760 operator-hours of coverage per year. This is the demand side of the staffing problem, independent of how many people the utility employs.Answer: 1,840 hours.
40 hours per week x 52 weeks = 2,080 paid hours. Subtract 160 hours of leave and 80 hours of training: 2,080 - 160 - 80 = 1,840 available hours per operator.Answer: 5 operators.
8,760 / 1,840 = 4.76 operators. Because a partial operator cannot stand a shift, round up. Four operators supply only 4 x 1,840 = 7,360 hours, which is short of 8,760, so 5 is the smallest workable number.Answer: 1,400 hours.
4 operators x 1,840 hours = 7,360 hours of coverage. Uncovered = 8,760 - 7,360 = 1,400 hours per year.Answer: $59,850.
1,400 hours x $42.75 per hour = $59,850 in overtime per year.Answer: $79,226.40.
Benefits = $60,020 x 0.32 = $19,206.40. Full cost = $60,020 + $19,206.40 = $79,226.40 per year.Answer: $19,376.40.
$79,226.40 - $59,850 = $19,376.40 more per year for the hire. The comparison is close enough that the board would also weigh fatigue, turnover, and what happens when an operator on the small crew is sick.Answer: 50 hours.
Each operator needs 20 contact hours every two years, which is 10 contact hours per year. For 5 operators: 5 x 10 = 50 contact hours per year.Answer: $4,750.
50 contact hours x $95 per hour = $4,750 per year, or $950 per operator.Answer: 4 positions.
12 employees x 1/3 = 4 positions becoming retirement-eligible within the decade. Talbrook would need a hiring and training plan that starts well before those retirements.Answer: $396,132.
Each operator costs $79,226.40 from item 6. For five: 5 x $79,226.40 = $396,132 per year.Answer: $73.36.
$396,132 / 5,400 connections = $73.358, which rounds to $73.36 per connection per year, or about $6.11 per month on a customer's bill.Answer: Payroll per connection.
Accept either choice when the reasoning is sound. The stronger case is payroll per connection, because the board's real question is what the staffing plan does to a customer bill, and per-connection cost is the quantity that answers it directly. Total payroll is the right quantity for a budget line but does not indicate whether the cost is reasonable for a system of this size.Answer: Accept any two supported paths.
Look for two genuinely different routes, each with a stated advantage. Common correct answers include a high school diploma followed by on-the-job training and a state licensing exam, which lets a person earn while qualifying; a community college certificate or associate degree in water technology, which shortens the on-the-job time required for higher license classes; a registered apprenticeship that pairs paid work with classroom hours; and a four-year engineering or environmental science degree, which opens design and management roles alongside plant operations. All are legitimate routes into the field.
Differentiation
Support
Give students a completed hours ladder for the fictional Talbrook plant showing 40 hours per week, then 2,080 hours per year, then 1,840 available hours, with the subtraction already carried out, so items 1 through 4 stay focused on the coverage comparison. Provide item 6 partly set up as $60,020 + (0.32 x $60,020) so the benefit calculation is a single step.
Extension
Ask students to build a general model for the fictional utility: write a function that gives the number of operators needed for a plant staffed h hours per day, using the same 1,840 available hours per operator. Have them evaluate the model for a plant staffed 16 hours per day and explain why the answer is not simply two-thirds of item 3.
ELL supports
Pre-teach "coverage," "full-time equivalent," "overtime," and "contact hour" using a weekly shift chart for the fictional plant with the hours shaded. Provide a two-column comparison frame for item 7 labeled "cost of overtime" and "cost of a new position," and sentence starters for items 13 and 14, such as "This quantity is better for the board because ___."
Extensions
Have students interview or research one licensed operator's route into the field, then place that route on a timeline against the fictional Talbrook hiring plan from item 10. Students can also rebuild items 5 through 7 using the 10th percentile and 90th percentile operator wages of about $39,110 and $91,060 in place of the median, then describe how the hiring decision changes when the wage assumption changes.