Question

A running track design is composed of two half circles connected by two straight-line segments. Garrett is jogging on the inner lane (with radius r) while Devin is jogging on the outer (with radius R). If r= 30 meters and R= 33 meters, how much longer does Devin have to run to complete one lap?​

Answer 1

18.86 m

Explanation:

From the given question, both covers the same distance of the straight line segment.

For the inner lane,

length of arc of its semicircle =
`\pi`r

= 30 x
`(22)/(7)`

= 94.2857

So that,

the total length for the two halves of the inner lane = 2 x 94.2857

= 188.5714 m

For the outer lane,

length of arc of its semicircle =
`\pi`r

= 33 x
`(22)/(7)`

= 103.7143

The total length for the two halves of the outer lane = 2 x 103.7143

= 207.4286 m

The difference between the two = 207.4286 - 188.5714

= 18.8572 m

Therefore, Devin would run 18.86 m more to complete one lap.