A ralload crew can lay 5 miles of track each day. They need to lay 135 miles of track. The length, \( L \) ( In miles), that is lieft to lay after d days is given by the following linction. \[ L(d)=135-5 d \] answer the following questions. (a) How many days will it take the crew to lay all the track? \( \square \) thys (b) How many miles of track does the crew have lett to lay after 18 days? \( \square \) miles
Upstudy AI Solution
Answer
Solution

Sign in to Unlock Answers for Free!
A Learning Platform Trusted by Millions of Real Students and Teachers.

Answered by UpStudy AI and reviewed by a Professional Tutor
The Deep Dive
To find out how many days it will take the crew to lay all the track, we set \( L(d) \) to zero, since we want to lay all 135 miles. Thus, we solve the equation: \[ 0 = 135 - 5d \] Rearranging gives: \[ 5d = 135 \quad \Rightarrow \quad d = \frac{135}{5} = 27 \] So, it will take the crew **27 days.** For part (b), to find out how many miles of track are left to lay after 18 days, we substitute \( d = 18 \) into the function: \[ L(18) = 135 - 5 \times 18 = 135 - 90 = 45 \] Therefore, after 18 days, the crew has **45 miles** of track left to lay.