Question 18

Narrow square paths ABCD and abcd have sides of $$200\text{ m}$$ and $$100\text{ m}$$. Two persons P and Q are initially located at a and A respectively. They both start walking in a clockwise sense.<br>Starting from the same initial positions P and Q walk at $$1\text{ m/s}$$ and $$2\text{ m/s}$$ respectively, find the shortest distance (in m) between them.
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Correct Answer: 50

Solution

The two paths are concentric squares whose parallel sides are $$50\text{ m}$$ apart, so P and Q can never be closer than 50 m. At $$t = 50\text{ s}$$, P has walked 50 m from a to the middle of side ab and Q has walked 100 m from A to the middle of side AB, directly opposite. So the shortest distance is 50 m.

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