Chapter 8, Problem 34E

Solution

Toidentify:The rate at which each of you is traveling.You travel 10 mi on your bicycle in the same amount of time it takes your friend to travel 8 mi on his bicycle. If your friend rides his bike 2 mi/h slower than you ride your bike.

Given information:

The given is $d_1=10mi,d_2=8mi$

The speed of my friend is $2mi/h$ slower than me.

Explanation:

Consider the given function.

Let us assume that I ride my bicycle with the speed of $xmi/h$ then the speed of my friend will be $\left(x-2\right)mi/h$

The formula for relation between speed and distance with similar time

  $\frac{d_1}{x_1}=\frac{d_2}{x_2}$

Substitute the value.

  $\frac{10}{x}=\frac{8}{x-2}$

Solve the above equation.

  $\begin{array}{l}10\left(x-2\right)=8x\\ 10x-20=8x\\ 10x-8x=20\\ 2x=20\\ x=10\end{array}$

Put the value of $x$ into $x-2$ it is help to determine the my friend bike speed.

  $\begin{array}{l}x-2\\ 10-2\\ 8mi/h\end{array}$

Thus the speed of mine and my friend $10mi/h$ and $8mi/h$ respectively