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

Did two already, don’t know how to do this one because of negatives-example-1

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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}

User JoniVR
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