# Oh, wait wind disturbed question.

Classical Mechanics Level 5

Two cyclists, Mike and Josh, simultaneously started toward each other from two town $$D$$ apart. Josh rode at $$v_{j}$$, and Mike rode at $$v_{m}$$. Before departure, a fly landed on Josh's nose and started to fly toward Mike the moment Josh departs. When it reached Mike, it immediately turned back and flew towards Josh. As soon as the fly reached Josh, it turned back again, and so on. Air speed of fly was always $$v_{f}$$ and the wind blew always toward Mike with constant velocity $$v_{w}$$. Find the total distance $$S$$ flown by the fly until the cyclists met.

Details:

• $$D$$=$$24 km$$ , $$v_{j}$$=$$25 km/h$$ , $$v_{m}$$=$$15 km/h$$ , $$v_{f}$$=$$30 km/h$$ , $$v_{w}$$=$$10 km/h$$

• $$S$$ is in $$km$$

• Gravity is ignored in every aspect.

• The problem is from physics olympiad.

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