A railroad crew can lay 6 miles of track each day. They need to lay 168 miles of track. The length, $$ L $$ following function. $$ L(d)=168-6 d $$ Answer the following questions. (a) How many miles of track does the crew have left to lay after 17 days? $$ 66[ $$ miles (b) How many days will it take the crew to lay all the track? $$ \square $$ days

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1. **Determine the amount of track left after 17 days:**

We are given the function  
   $$
   L(d)=168-6d
   $$
   where $$ d $$ represents the number of days. For $$ d = 17 $$:
   $$
   L(17)=168-6(17)
   $$
   Calculate $$ 6(17) $$:
   $$
   6 \times 17 = 102
   $$
   Now subtract from 168:
   $$
   L(17)=168-102=66
   $$
   So, after 17 days, the crew has laid track leaving  
   $$
   L(17)=66 \text{ miles}
   $$  
   of track still to lay.

2. **Determine the number of days needed to lay all the track:**

To find the number of days when all the track has been laid, we set $$ L(d) $$ equal to 0:
   $$
   168-6d=0 
   $$
   Solve for $$ d $$:
   $$
   6d = 168
   $$
   Divide both sides by 6:
   $$
   d = \frac{168}{6}=28
   $$
   It will take the crew  
   $$
   28 \text{ days}
   $$
   to lay all the track.
After 17 days, the crew has 66 miles of track left to lay. It will take them 28 days to complete all the track.

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