Question

Supervisor a earns a flat rate of $25 per hour, while supervisor b earns $20 per hour for the first 30 hours and then 50% more for each additional hour within a work week. if both supervisors worked the same number of hours and earned the same pay during one work week, how many hours did each supervisor work in that week?

Answer 1

a: 25h
b:20h+30(h-30)
25h=20h+30(h-30)
5h=30h-30^2
-25h=-30^2
25h=30^2
h=900/25

Answer 2

Each supervisor worked 60 hours during the week.

Explanation:

Supervisor a:

Supervisor a earns a flat rate of $25 per hour.

So his earnings are

`E_(a)(t) = 25t`

In which t is the number of hours he works.

Suppervisor b:

$20 per hour for the first 30 hours and then 50% more for each additional hour within a work week.

Piecewise function. So

`E_(b)(t) = \left \{ {{20t, t \leq 30} \atop {20t + 10(t - 30)}, t > 30} \right`

If both supervisors worked the same number of hours and earned the same pay during one work week, how many hours did each supervisor work in that week?

Can only happen after 30 hours,s o this is when

`25t = 20t + 10(t - 30)`

`25t = 20t + 10t - 300`

`5t = 300`

`t = (300)/(5)`

`t = 60`

Each supervisor worked 60 hours during the week.