Question

You travel 10 mi on your bicycle in the same amountof time it takes your friend to travel 8 mi on hisbicyde. If your friend rides his bike 2 mi/h slowerthan you ride your bike, find the rate at which eachof you is traveling

Answer 1

We have:

x = rate you. 10 miles ---> t times

y = rate your friend. 8 miles ---> t times

and y = x - 2

then, the equation is:

$\frac{10}{x}=\frac{8}{y}$

solve the system:

$\begin{gathered} \frac{10}{x}=\frac{8}{y} \\ \frac{10}{x}=\frac{8}{x-2} \\ 10\mleft(x-2\mright)=x\cdot\: 8 \\ 10x-20=x\cdot\: 8 \\ 10x-20+20=x\cdot\: 8+20 \\ 10x=x\cdot\: 8+20 \\ 10x-x\cdot\: 8=x\cdot\: 8+20-x\cdot\: 8 \\ 2x=20 \\ \frac{2x}{2}=\frac{20}{2} \\ x=10 \end{gathered}$

then for y:

$\begin{gathered} y=x-2 \\ y=10-2 \\ y=8 \end{gathered}$

Answer:

10 mi/h and the friend 8 mi/h