A Different Version of the Cyclists' Problem

Algebra Level 5

Two cyclists, A\displaystyle A and B\displaystyle B, 100\displaystyle 100 metres apart, start cycling towards each other with 20ms1\displaystyle 20 \text{ms}^{-1} and 30ms1\displaystyle 30 \text{ms}^{-1} respectively.

As you would have expected, a fly sits on the nose of A\displaystyle A, and as they start, starts moving towards B\displaystyle B, and then back and forth all the way till it gets smashed between the noses of A\displaystyle A and B\displaystyle B. The fly maintains a constant speed of 39ms1\displaystyle 39 \text{ms}^{-1}.

How much distance of the total, in metres, did the fly fly from B\displaystyle B towards A\displaystyle A?

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