Question

A construction crew needs to pave a road that is 209 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)=209-8d

Question a.)
If 154 miles of the road is left to be paved, how many days has the crew been paving the road?

Question b.)
How many miles of the road does the crew have left to pave after 13 days?

Answer 1

a) 6 7/8 days

b) 105 miles

Explanation:

Given that L(d) = 209 -8d miles of road remain to be paved after d days, you want to know (a) the number of days paving if 154 miles remain, and (b) remaining miles after 13 days.

a) Paving days

We want to find d such that L(d) = 154.

L(d) = 154

209 -8d = 154 . . . . . . substitute for L(d)

209 -154 = 8d . . . . . add 8d-154

55/8 = d = 6 7/8 . . . divide by 8

The crew has been paving for 6 7/8 days if 154 miles remain.

b) Remaining miles

After 13 days, the remaining miles will be ...

L(13) = 209 -8·13 = 209 -104

L(13) = 105

After 13 days, the crew has 105 miles left to pave.

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