Let Y be your velocity rate and F be the velocity rate of your friend. Since your friend rides his bike 2 mi/h slower than you, we can write:
[tex]F=Y-2\ldots(a)[/tex]Now, in 10 minutes, your friend travel 8 miles. Then, his velocity rate is
[tex]F=\frac{8mi}{10\min }[/tex]but, in order to use this result, we need to convert miles/minutes into miles/hour. Lets convert it:
[tex]\begin{gathered} \frac{8mi}{10\min}=\frac{8mi}{10\min}(\frac{60\min }{1h}) \\ \text{then} \\ \frac{8mi}{10\min}=48\frac{mi}{h} \end{gathered}[/tex]Then, the friend's velocity rate is
[tex]F=48\frac{mi}{h}\ldots(b)[/tex]Finally, by substituting this result into equation (a), we have
[tex]\begin{gathered} 48=Y-2 \\ \text{then,} \\ Y=48+2 \\ Y=50\frac{mi}{h} \end{gathered}[/tex]Therefore, the answers are:
[tex]\begin{gathered} \text{Your velocity rate is} \\ Y=50\frac{mi}{h} \\ \text{the velocity rate of your Friend is} \\ F=48\frac{mi}{h} \end{gathered}[/tex]