Question

Did two already, don’t know how to do this one because of negatives

Answer 1

The distance to the destination is given by a linear function of the total driving time. A general linear model can be written as:

`D(t)=m\cdot t+b`

Where m and b are parameters. From the problem, we know that:

Driving time (minutes) Distance to destination (miles)

45 64.0

63 50.5

Using the model above and the table values, we construct the system of equations:

`\begin{gathered} 64.0=45\cdot m+b \\ 50.5=63\cdot m+b \end{gathered}`

If we subtract these two equations:

`\begin{gathered} 64.0-50.5=45\cdot m-63\cdot m+b-b \\ 13.5=-18\cdot m \\ m=-(3)/(4) \end{gathered}`

Now, we can use the first equation to calculate b:

`\begin{gathered} 64.0=-45\cdot(3)/(4)+b \\ b=97.75 \end{gathered}`

Our linear model is:

`D(t)=-0.75\cdot t+97.75`

For t = 71 minutes:

`\begin{gathered} D(71)=-0.75\cdot71+97.75 \\ D(71)=44.5\text{ miles} \end{gathered}`