Question

A construction crew needs to pave a road that is 202 miles long. The crew paves 7 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) =202-7dIf 139 miles of road is left to be paved how many days has the crew been paving the road?How many miles of road does the crew have left to pave after 11 days?

Answer 1

We have the following function that tells us how many miles there are left to be paved:

`L(d)=202-7d\text{.}`

For the first part, we are told that there are 139 miles of road left to be paved, and we want to know how many days have passed. This leads us to the follwoing equation:

`202-7d=139.`

In order to solve it, let's add 7d to both sides:

`202=139+7d\text{.}`

Now, let's subtract 139 from both sides:

`63=7d\text{.}`

Finally, let's divide both sides by 7 to obtain the value of d:

`d=9,`

which means that, if 139 miles are left to be paved, the crew has been working for 9 days.

For the second part, we want to know how many miles of road there are left to be paved if the crew has been working for 11 days. For this, we must determine L(11):

`L(11)=202-7(11)=202-77=125.`

So the crew will have 125 miles left to pave if they've been working for 11 days.