Question

a construction crew needs to pave a road that is 205 miles long. the crew paves 7 miles of the road each day. the length, l (in miles), that is left to be paved after d days is given by the following function.
l(d) = 205 - 7d
answer the following questions.
(a) if 149 miles of the road is left to be paved, how many days has the crew been paving the road?
days
(b) how many miles of the road does the crew have left to pave after 13 days?
miles

Explanation:

Part (a)

Step1: Set up the equation

We know that \( L(d) = 205 - 7d \), and we are given that \( L(d)=149 \). So we set up the equation \( 149 = 205 - 7d \).

Step2: Solve for \( d \)

First, subtract 205 from both sides: \( 149 - 205=- 7d \), which simplifies to \( - 56=-7d \). Then divide both sides by - 7: \( d=\frac{-56}{-7} = 8 \).

Step1: Substitute \( d = 13 \) into the function

We use the function \( L(d)=205 - 7d \). Substitute \( d = 13 \) into it, so we have \( L(13)=205-7\times13 \).

Step2: Calculate the value

First, calculate \( 7\times13 = 91 \). Then, \( 205-91 = 114 \).

Answer:

8

Part (b)