Question:
A jogging park has two identical circular tracks touching each other, enclosed by a rectangular track tangent to both circles. A jogger A runs around rectangle, jogger B runs a figure eight along circles. How much faster must B run to finish together with A?
A jogging park has two identical circular tracks touching each other, enclosed by a rectangular track tangent to both circles. A jogger A runs around rectangle, jogger B runs a figure eight along circles. How much faster must B run to finish together with A?
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Compare total path lengths to find required relative speed.
Updated On: Jul 31, 2025
- 3.88%
- 4.22%
- 4.44%
- 4.72%
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The Correct Option is C
Solution and Explanation
Let circle radius $r$. Rectangle length = $4r$, width = $2r$, perimeter = $12r$. A’s distance = $12r$. B’s distance = $4\pi r$. Percent faster = $\frac{4\pi r - 12r}{12r} \times 100 \approx 4.44%$.
\[
\boxed{4.44%}
\]
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