Chapter 12.6, Problem 9P

To determine

To find: speed of each person travelling.

Answer to Problem 9P

The speed of Cindy is $8mi/h$ and the speed of Olaf is $6mi/h$ .

Explanation of Solution

Given information:

Cindy is travelling to west with the speed of $2mi/h$ faster than Olaf and Olaf is travelling to south.

Formula:

Pythagoras theorem $h^2=\sqrt{p^2+b^2}$ where $p$ is speed of Olaf and $b$ is speed of Cindy.

The quadratic equation $\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ where $a,b,c$ is any constant.

Calculation:

Consider the speed of Olaf be $x$ and the speed of Cindy be $\left(x+2\right)mi/h$ .

After one hour, they both are $10mi$ apart.

Recall that the Pythagoras theorem $h^2=\sqrt{p^2+b^2}$ .

Therefore $10mi=x^2+{\left(x+2\right)}^2\Rightarrow 10=x^2+x^2+4+2x\Rightarrow x^2+2x-48=0$ .

Recall that quadratic equation where $a=1,b=2,c=-48$ .

  $\begin{array}{l}\frac{-2\pm \sqrt{2^2+4\times 1\times 48}}{2}\Rightarrow \frac{-2\pm \sqrt{4+192}}{2}=0\Rightarrow x=\frac{-2\pm \sqrt{196}}{2}=0\\ \Rightarrow x=\frac{-2+14}{2},\frac{-2-14}{2}\Rightarrow x=6,-8.\end{array}$

Therefore the speed of Olaf be $6mi/h$ and the speed of Cindy be $\left(x+2\right)mi/h\Rightarrow \left(6+2\right)mi/h$ .