Question

a railroad crew can lay 7 miles of track each day. they need to lay 196 miles of track. the length, l (in miles), that is left to lay after d days is given by the following function. l(d) = 196 - 7d answer the following questions. (a) how many miles of track does the crew have left to lay after 17 days? miles (b) how many days will it take the crew to lay all the track? days

Explanation:

Part (a)

Step1: Substitute \( d = 17 \) into \( L(d) \)

We have the function \( L(d)=196 - 7d \). To find the miles left after 17 days, we substitute \( d = 17 \) into the function. So we calculate \( L(17)=196-7\times17 \).

Step2: Calculate the value

First, calculate \( 7\times17 = 119 \). Then, \( 196-119 = 77 \).

Part (b)

Step1: Set \( L(d)=0 \)

When all the track is laid, the length left \( L(d) = 0 \). So we set up the equation \( 0 = 196-7d \).

Step2: Solve for \( d \)

Add \( 7d \) to both sides of the equation: \( 7d=196 \). Then divide both sides by 7: \( d=\frac{196}{7}=28 \).

Answer:

(a) 77 miles
(b) 28 days