Jill has a job like Jack’s except that she makes $\$10/\text{hr}$ after six hours. 

1. Find $J(t)$, Jill’s earnings after t hours of work.

   Answer (a):

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

2. Crown’s job pays $\$6/\text{hr}$ for the first $8$ hours and then $\$12/\text{hr}$ after that. What is $C(t)$, Crown’s earnings after t hours on the job?

   Hint (b):

   Use the same thinking as in (a) above.

3. When will Jill make $\$46$?

   Hint (c):

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

4. Extension: When does Jill make more than Crown?

   Answer (d):

   When is $30+10\left(t-6\right)>48+12\left(t-8\right)$ AND $6t<30+10(t-6)$?