Question

two cyclists start at the same point and travel in opposite directions. one cyclist travels 8 mi/h faster than the other. If the two cylists are 210 miles apart after 5 hours, what is the rate of each cyclist?

Answer 1

The two cyclists are 210 miles apart after 5 hours, their added speed is:

`(210mi)/(5h)=42\text{ mi/h}`

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:

`x+x+8=42`

Note that we are adding their speed because they are traveling in opposite directions, so their speeds add up.

We solve for x:

`\begin{gathered} 2x+8=42 \\ 2x=42-8 \\ 2x=34 \\ x=(34)/(2) \\ x=17 \end{gathered}`

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