Chapter 1, Problem 11CR

To determine

How far can you ride your bike in $45$ minutes.

Answer to Problem 11CR

You can ride your bike in $45$ minutes is $15.75$ miles.

Explanation of Solution

Given information: You ride your bike and measure how far you travel .The given function is $g(x)=-3{(x+3)}^2$ .

Calculation: The linear function distance in terms of time.

From given information we find the coordinates:

  $\mathrm{P}(10,3.5),\mathrm{Q}(30,10.5)$

Slope of line is:

  $m=\frac{10.5-3.5}{30-10}=\frac{7}{20}$

Equation of line is:

  $\begin{array}{l}y-3.5=\frac{7}{20}(x-10)\\ 20y-70=7x-70\\ 20y=7x-70+70\\ y=\frac{7x}{20}=0.35x\end{array}$

To find how far you are in $45$ minutes we put $x=45\mathrm{in}y=0.35x$ we get:

  $y=0.35\times 45=15.75$

Therefore you can ride your bike in $45$ minutes is $15.75$ miles.