a) 8 days b) 101 miles
1) Considering the function:
[tex]L(d)=209-9d[/tex]
2) Note that "d" stands for days, and "L" is the length. Based on that, we can plug into the function.
a) Let's plug into L, the number of paved miles, and then solve it for d
[tex]\begin{gathered} 137=209-9d \\ 137-209=209-209-9d \\ -72=-9d \\ \frac{-72}{-9}=\frac{-9d}{-9} \\ d=8 \end{gathered}[/tex]
So the crew has been paving the road for 8 days
b) Similarly, we're going also to plug into that d=12 to find the length
[tex]\begin{gathered} L(12)=209-9(12) \\ L(12)=209-108 \\ L(12)=101 \end{gathered}[/tex]
Note that, the crew has left to pave after 12 days, 101 miles.
Notice that the variable L always provides the remaining number of miles to be paved.
3) Hence, the answer is a) 8 days b) 101 miles
