Speed!
A car is moving at a constant speed of 40km/h along a straight road which heads towards a large vertical wall and makes a sharp 90 degree turn by the side of the wall. A fly flying at a constant speed of 100km/h, starts from the wall towards the car at an instant when the car is 20km away, flies until it reaches the glass-pane of the car and returns to the wall at the same speed. It continues to fly between the car and the wall till the car makes the 90degree turn. How many trips has it made between the car and the wall?
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1 solution
Assume the car and fly are 0 -dimensional objects (points). No matter how close the car gets to the wall, the fly can always take more trips between them. Thus, even though the car hits the wall, the fly took infinitely many trips. This seems to conflict common sense, that the fly can only take so many journeys in a fixed amount of time; the resolution to this apparent paradox is that the trips approach an infinitesimal time.