Answer:
• The rate of the first cyclist is 21 mi/h
,• The rate of the second cyclist is 16 mi/h.
Explanation:
• Let the rate of the first cyclist = x mi/h.
One cyclist travels 5 mi/h slower than the other, therefore:
• The rate of the second cyclist = (x-5) mi/h.
[tex]\begin{gathered} \text{Distance}=\text{Rate}\times Time \\ \text{The distance covered by the first cyclist: }d_1=5x \\ \text{The distance covered by the }\sec ond\text{ cyclist: }d_2=5(x-5) \end{gathered}[/tex]The distance between the two cyclists = 185 miles.
Since they move in opposite directions, we add the distances.
[tex]\begin{gathered} 5x+5(x-5)=185 \\ 5x+5x-25=185 \\ 10x=185+25 \\ 10x=210 \\ x=210\div10 \\ x=21\text{ mi/h} \end{gathered}[/tex]Therefore, the rate of the first cyclist is 21 mi/h and the rate of the second cyclist is 16 mi/h.
