Question

Robin worked his 40 regular hours last week plus 20 overtime hours at the time-and-a-half rate. His gross pay was $16,203. What is his regular hourly rate?

Answer 1

His rate is a whopping $231.47 per hour.

:)

Explanation:

We can conclude that.

`r*t_1=p_(reg)` is the gross pay from his regular hours.

`1.5r*t_2=p_(ovt)` is the gross pay from his overtime hours.

So all together we can say

`(r*t_1)+(1.5r*t_2)=p`

We are looking for his hourly rate.

Lets solve for
`r`.

Multiply the terms in the parenthesis.

`rt_1+1.5rt_2=p`

Factor
`r` out of
`rt_1`.

`r(t_1)+1.5rt_2=p`

Factor
`r` out of
`1.5rt_2`.

`r(t_1)+r(1.5t_2)=p`

Factor
`r` out of
`r(t_1)+r(1.5t_2)`.

`r(t_1+1.5t_2)=p`

Divide each term in
`r(t_1+1.5t_2)=p` by
`t_1+1.5t_2` and simplify.

`(r(t_1+1.5t_2))/(t_1+1.5t_2) =(p)/(t_1+1.5t_2)`

Simplify the left side. Cancel the common factor of
`t_1+1.5t_2`

`r=(p)/(t_1+1.5t_2)`

Now we have an equation to find his regular hourly rate.

We are given

`p=16203`

`t_1=40`

`t_2=20`

Lets plug these numbers into our equation for
`r`.

`r=(16203)/(40+1.5*20)`

`r=(16203)/(70)`

`r=231.47`