### Home > PC3 > Chapter 7 > Lesson 7.1.1 > Problem7-13

7-13.

Crane makes $\5/\text{h}$ for the first six hours on the job and then $\10/\text{h}$ after that. Jill’s job pays $\6/\text{h}$ for the first eight hours and then $\9/\text{h}$ after that. Homework Help ✎

1. Write the equation of a function that models Crane’s earnings after t hours.

Make a table for the first $12$ hours.
Note that you will need to write the equation of a piecewise-defined function since there are two different pay rates.

2. Write the equation of a function that models Jill’s earnings after $t$ hours.

$J(t) = \left\{ \begin{array}{l l} 6t & \quad \text{for }0\le t \le 8\\ 48+10(t-8) & \quad \text{for }t>8 \end{array} \right.$

3. When will Jill make $\46$?

You know that in $6$ hours
Jill will have $\30$.
So $30+10(t-6)=46$.
Solve for $t$.

4. When does Crane make more than Jill?

After $6$ hours, Crane has earned $\30$ and Jill has earned $\36$.
After $8$ hours, Crane has earned $\50$ and Jill has earned $\48$.