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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

Ask by Sandoval Edwards. in the United States
Mar 16,2025

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(a) It takes 27 days for the crew to lay all the track. (b) After 18 days, there are 45 miles of track left to lay.

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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.

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