Cathy is paid at a rate of K7.20 per hour for a basic hour-week of 70 hours. She is paid time-and-a-half for over-time during 4 hours on Saturday and 2 hours.
(a) How many hours does Cathy work in a fortnight?
(b) Calculate overtime earned during the week.
(c) Calculate over-time earned during the weekend.
(d) Find the total wage she earned in that fortnight.
Answer (2)
Calculate total hours worked: 160 + 4 + 2 = 166 hours.
Calculate overtime hours during the week: 160 − ( 70 × 2 ) = 20 hours.
Calculate overtime hours during the weekend: 4 + 2 = 6 hours.
Calculate total wage: ( 140 × 7.20 ) + ( 20 × 7.20 × 1.5 ) + ( 6 × 7.20 × 1.5 ) = K 1288.80 .
The total wage she earned in that fortnight is K 1288.80 .
Explanation
Understanding Cathy's Earnings Let's break down Cathy's earnings step by step to understand how her total wage is calculated. We'll start by identifying all the components of her pay: regular hours, overtime hours during the week, and overtime hours during the weekend.
Total Hours Worked First, we need to calculate the total hours Cathy worked in the fortnight. She worked 160 hours during the week and an additional 4 hours on Saturday and 2 hours on Sunday. So, the total hours worked are: 160 + 4 + 2 = 166 hours
Overtime Hours During the Week Next, let's find the overtime hours Cathy earned during the week. Her basic work week is 70 hours, so for a fortnight, it's 70 × 2 = 140 hours. She worked 160 hours during the week, so her overtime hours during the week are: 160 − 140 = 20 hours
Overtime Hours During the Weekend Now, let's calculate the overtime hours Cathy earned during the weekend. She worked 4 hours on Saturday and 2 hours on Sunday, so her overtime hours during the weekend are: 4 + 2 = 6 hours
Calculating the Overtime Rate Cathy's regular hourly rate is K7.20. Her overtime rate is time-and-a-half, which means it's 1.5 times her regular rate. So, the overtime rate is: K 7.20 × 1.5 = K 10.80 per hour
Calculating Regular Pay Now, we can calculate Cathy's earnings. Her regular pay for the fortnight is the basic hours multiplied by her regular hourly rate: 140 hours × K 7.20 per hour = K 1008.00
Calculating Overtime Pay During the Week Her overtime pay during the week is the overtime hours during the week multiplied by the overtime rate: 20 hours × K 10.80 per hour = K 216.00
Calculating Overtime Pay During the Weekend Her overtime pay during the weekend is the overtime hours during the weekend multiplied by the overtime rate: 6 hours × K 10.80 per hour = K 64.80
Calculating Total Wage Finally, we can find Cathy's total wage for the fortnight by adding her regular pay and her overtime pay: K 1008.00 + K 216.00 + K 64.80 = K 1288.80 Therefore, Cathy earned a total wage of K1288.80 in that fortnight.
Final Answer Therefore, Cathy's total wage for the fortnight is K1288.80.
Examples
Understanding wage calculations with overtime is crucial in many real-world scenarios. For instance, in construction, employees often work overtime to meet deadlines. Calculating their total earnings accurately ensures fair compensation and compliance with labor laws. Similarly, in healthcare, nurses and doctors frequently work extended hours, making precise overtime calculations essential for both the employee's financial well-being and the employer's budgeting. This problem demonstrates the importance of understanding how regular pay and overtime rates combine to determine an individual's total earnings.
Cathy worked a total of 146 hours in the fortnight, with 20 hours of overtime during the week and 6 hours over the weekend. Her total earnings amounted to K1288.80, calculated from regular and overtime pay. Thus, Cathy earned K1288.80 in total for her work in that fortnight.
;
