Question

A park has two gates, Gate 1 and Gate 2. These two gates are connected via two alternate paths. If one takes the first path from Gate 1, they need to walk $80\text{m}$ towards east, then $80\text{m}$ towards south, and finally $20\text{m}$ towards west to arrive at Gate 2. The second path is a semi-circle connecting the two gates, where the diameter of the semi-circle is the straight-line distance between the two gates.

A person walking at a constant speed of $5\text{ km/h}$ enters the park through Gate 1, walks along the first path to reach Gate 2 and then takes the second path to come back to Gate 1.

Which of the following is the CLOSEST to the time the person takes, from entering the park to coming back to Gate 1, if she never stops in between?

Accepted Answer

A. Path 1 length $= 80 + 80 + 20 = 180	ext{ m}$. Straight line distance between Gate 1 and Gate 2: East displacement $= 80 - 20 = 60	ext{ m}$. South displacement $= 80	ext{ m}$. Diameter $D = \sqrt{60^2 + 80^2} = 100	ext{ m}$. Path 2 (semi-circle) length $= \frac{\pi D}{2} = 50\pi \approx 157	ext{ m}$. Total distance $= 180 + 157 = 337	ext{ m}$. Speed $= 5	ext{ km/h} = \frac{5000}{60} = \frac{250}{3}	ext{ m/min}$. Time taken $= \frac{337}{250/3} = \frac{1011}{250} \approx 4.044	ext{ minutes} \approx 4	ext{ minutes}$.

Walking time between park gates

Explanation

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