# A Different Version of the Cyclists' Problem

Algebra Level 5

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

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

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

×