The two cyclists are 210 miles apart after 5 hours, their added speed is:
[tex]\frac{210mi}{5h}=42\text{ mi/h}[/tex]We will call the speed of cyclist one x,
and since the other cyclist travels 8mi/h faster, the speed of the second cyclist is: x+8.
And when we add these speeds or rates, we have to get the added speed of 42mi/h:
[tex]x+x+8=42[/tex]Note that we are adding their speed because they are traveling in opposite directions, so their speeds add up.
We solve for x:
[tex]\begin{gathered} 2x+8=42 \\ 2x=42-8 \\ 2x=34 \\ x=\frac{34}{2} \\ x=17 \end{gathered}[/tex]One cyclist is traveling at 17mi/h.
And the other cyclist will travel 8mi/h faster:
17mi/h + 8mi/h=25mi/h
Answer: 17mi/h and 25mi/h
