Question

a railroad crew can lay 6 miles of track each day. they need to lay 162 miles of track. the length, l (in miles), that is left to lay after d days is given by the following function.
l(d) = 162 - 6d
answer the following questions.
(a) how many days will it take the crew to lay all the track?
square days
(b) how many miles of track does the crew have left to lay after 18 days?
square miles

Explanation:

Part (a)

Step 1: Understand the problem

We need to find the number of days \( d \) when all the track is laid, which means the length left \( L(d) = 0 \). The function is \( L(d)=162 - 6d \).

Step 2: Set up the equation

Set \( L(d) = 0 \), so we have the equation \( 0=162 - 6d \).

Step 3: Solve for \( d \)

Add \( 6d \) to both sides of the equation: \( 6d=162 \). Then divide both sides by 6: \( d=\frac{162}{6} = 27 \).

Part (b)

Step 1: Understand the problem

We need to find the length of track left \( L(d) \) after \( d = 18 \) days. The function is \( L(d)=162 - 6d \).

Step 2: Substitute \( d = 18 \) into the function

Substitute \( d = 18 \) into \( L(d)=162 - 6d \), we get \( L(18)=162-6\times18 \).

Step 3: Calculate the value

First, calculate \( 6\times18 = 108 \). Then subtract from 162: \( L(18)=162 - 108=54 \).

Answer:

(a) 27 days
(b) 54 miles