Discussion
Two friends A and B play hide and seek. Initially they are standing at same position. A runs in North for 20 m and B runs in South for 15 m. A then runs in West for 40 m and B runs in East for 10 m. A then runs in North for 15 m and B also runs in North for 50 m. How far apart are the two friends now?
Answer: C
The friends are 50 m apart.
Take the start as the origin, East as +x and North as +y.
\[ \begin{aligned} A &= (0, 20) \to (-40, 20) \to (-40, 35) \\ B &= (0, -15) \to (10, -15) \to (10, 35) \end{aligned} \]
Both end at the same height, 35 m North of the start, so the distance between them is the horizontal gap \(10 - (-40) = 50\) m. 35 m is their common northward position, and 60 m comes from adding the East-West distances as if both went the same way.
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