Questions: A construction crew needs to pave a road that is 205 miles long. The crew paves 8 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)=205-8d Answer the following questions. (a) How many miles of the road does the crew have left to pave after 12 days? miles (b) If 141 miles of the road is left to be paved, how many days has the crew been paving the road? days

A construction crew needs to pave a road that is 205 miles long. The crew paves 8 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)=205-8d Answer the following questions. (a) How many miles of the road does the crew have left to pave after 12 days? miles (b) If 141 miles of the road is left to be paved, how many days has the crew been paving the road? days
Transcript text: A construction crew needs to pave a road that is 205 miles long. The crew paves 8 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. \[ L(d)=205-8 d \] Answer the following questions. (a) How many miles of the road does the crew have left to pave after 12 days? $\square$ miles (b) If 141 miles of the road is left to be paved, how many days has the crew been paving the road? $\square$ days
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Solution

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Solution Steps

To solve these problems, we will use the given function \( L(d) = 205 - 8d \).

(a) To find how many miles are left after 12 days, substitute \( d = 12 \) into the function and calculate \( L(12) \).

(b) To find how many days the crew has been paving when 141 miles are left, set \( L(d) = 141 \) and solve for \( d \).

Step 1: Calculate Miles Left After 12 Days

To find the number of miles left after 12 days, substitute \( d = 12 \) into the function \( L(d) = 205 - 8d \).

\[ L(12) = 205 - 8 \times 12 = 205 - 96 = 109 \]

Step 2: Calculate Days of Paving When 141 Miles Are Left

To find the number of days the crew has been paving when 141 miles are left, set \( L(d) = 141 \) and solve for \( d \).

\[ 141 = 205 - 8d \]

Rearrange the equation to solve for \( d \):

\[ 8d = 205 - 141 = 64 \]

\[ d = \frac{64}{8} = 8 \]

Final Answer

  • The number of miles left after 12 days is \(\boxed{109}\) miles.
  • The number of days of paving when 141 miles are left is \(\boxed{8}\) days.
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