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The problem in the image provides the following information:

- A railroad crew can lay 7 miles of track each day.
- They need to lay 196 miles of track.
- The length \( L(d) \), which is the miles left to lay after \( d \) days, is given by the function:
  \[
  L(d) = 196 - 7d
  \]
  where \( d \) is the number of days.

We need to solve the following questions:

**(a) How many miles of track does the crew have left to lay after 17 days?**

Using the formula \( L(d) = 196 - 7d \), substitute \( d = 17 \):

\[
L(17) = 196 - 7(17)
\]
\[
L(17) = 196 - 119
\]
\[
L(17) = 77 \text{ miles}
\]

So, the crew has 77 miles of track left after 17 days.

**(b) How many days will it take the crew to lay all the track?**

To find how many days it will take for the crew to lay all the track, set \( L(d) = 0 \) because all the track will be laid:

\[
0 = 196 - 7d
\]
Solving for \( d \):

\[
7d = 196
\]
\[
d = \frac{196}{7} = 28 \text{ days}
\]

Thus, it will take the crew 28 days to lay all the track.

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Would you like more details on any part of this solution? 

Here are 5 related questions you might find interesting:
1. What would the function look like if the crew laid 8 miles per day instead of 7?
2. How many miles would be left after 20 days of work?
3. If the crew works for 10 days, how many more days are required to complete the track?
4. How would the equation change if the initial length of track was 300 miles?
5. What happens to the equation if the crew's speed decreases over time?

**Tip**: Always double-check your units when working with word problems to avoid calculation errors.

A railroad crew can lay 7 miles of track each day. They need to lay 196 miles of track. The length L (in miles) left to lay after d days is given by the following function: L(d) = 196 - 7d. (a) How many miles of track does the crew have left to lay after 17 days? (b) How many days will it take the crew to lay all the track?

Solve a linear function problem where a railroad crew lays 7 miles of track each day. Learn how to calculate how many miles are left after 17 days and how many days it will take to lay all 196 miles of track. Suitable for Grades 7-9.

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