### Home > PC > Chapter 2 > Lesson 2.3.7 > Problem2-156

2-156.

Jack makes $\5/\text{hr}$ for the first six hours on the job and then $\8/\text{hr}$ after that. Explain why $J(t)$, Jack’s earnings after he works t hours, is:

$J ( t ) = \left\{ \begin{array} { l l } { 5 t } & { \text { for } 0 \leq t \leq 6 } \\ { 30 + 8 ( t - 6 ) } & { \text { for } t > 6 } \end{array} \right.$

For the first six hours, Jack makes $\5/\text{hr}$, meaning at the end of six hours, he has earned $30$. For anytime after six hours (where he has already earned $30$) he adds to the $30$ by making $\8$ times the number of hours worked over six hours.