Given:
The laps are 30
Total distance = 7.5 Kilometer
Find-:
The distance when bikes laps are 40
Explanation-:
The radius of the bike = x
The distance of one lap
[tex]=2\pi r[/tex]Where
[tex]r=\text{ Radius}[/tex]The distance of 30 laps is:
[tex]\begin{gathered} =2\pi r\times(30) \\ \\ =60\pi r \end{gathered}[/tex]The distance is 75 kilometers.
[tex]60\pi r=7.5[/tex]A kilometer is 4.65 miles.
So, distance is:
[tex]\begin{gathered} =7.5\times4.65 \\ \\ =34.875\text{ miles} \end{gathered}[/tex]The radius is:
[tex]\begin{gathered} 60\pi r=34.875\text{ miles} \\ \\ r=\frac{34.875}{60\times\pi} \\ \\ r=\frac{0.58125}{\pi} \\ \\ r=0.185\text{ miles} \end{gathered}[/tex]The distance of 40 laps is:
[tex]\begin{gathered} \text{ Distance }=40\times2\pi r \\ \\ \text{ Distance }=80\pi r \\ \\ \text{ Distance }=80\times\pi\times0.185 \\ \\ \text{ Distance }=46.5\text{ miles} \end{gathered}[/tex]The distance of the race is 46.5 miles
