Discussion
Ramesh runs around a circular park every day at a speed of 60 m/min. One day he runs along the diameter at the same speed and so crosses the park, needing 60 minutes less than usual. What is the diameter of the park?
Answer: A
At the same speed, the time saved is proportional to the distance saved. Running around the park covers the circumference; crossing it covers the diameter.
\[ \text{distance saved} = 2\pi r - 2r = 2r(\pi - 1) \]
Sixty minutes at 60 m/min is 3600 m:
\[ 2r(\pi - 1) = 3600 \]
With \( \pi = \tfrac{22}{7} \), so that \( \pi - 1 = \tfrac{15}{7} \):
\[ 2r \times \frac{15}{7} = 3600 \quad\Longrightarrow\quad 2r = \frac{3600 \times 7}{15} = 1680 \text{ m} \]
So the diameter is 1680 m and the radius 840 m. Note that \( 2r \) - the diameter itself - falls out of the algebra directly, with no need to find the radius first.
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