Question

Carole worked her 40 regular hours last week plus 5 overtime hours atthe time-and-a-half rate. Her gross pay was $451.25. What was herhourly rate?

Answer 1

Carole earned two different payments:

- for 40 regular hours

- for 5 overtime hours at time-and-a-half rate.

And we want to find out her hourly rate. The hourly rate is the amount payid for regular hours, so the regular payment is:

`P_r=40r`

Where "r" is the hourly rate and P_r is the payment for the regular hours.

The time-and-a-half rate menas that the payment for the overtime hours is 50% more than the normal rate, which means we need to multiply the original rate by (100% + 50%) or 1.5. So, the payment for the overtime is:

`P_o=5(1.5r)=7.5r`

The total payment is 451.25 and it is the sum of the regular and the overtime payments, so:

`\begin{gathered} P_r+P_o=451.25 \\ 40r+7.5r=451.25 \\ 47.5r=451.25 \\ r=(451.25)/(47.5) \\ r=9.5 \end{gathered}`

So, Carole hourly rate is $9.5 per hour.