1. The problem statement, all variables and given/known data A car is moving with a constant speed of 40 km/h along a straight road which heads towards a large vertical wall and makes a sharp 90° turn by side of the wall . A fly flying at a constant speed of 100 km/h , start 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 return to the wall at same speed. It continues until the car makes the 90° turn. how many trips has it made between the car and the wall ? 2. Relevant equations distance = speed * time 3. The attempt at a solution Suppose the car is at a distance 'x' away(at A) when the fly is at the wall(at O ) . The fly hit the glass pane at B, taking a time 't'. Then AB = (40km/h)t , OB = (100km/h)t Thus x = AB + OB = (140km/h)t t =x / 140 km/h OB = 5x / 7 The fly returns to the wall and during this time period car moves BC. The time taken by the fly in this return path is 5x /7 / 100 or x / 140 BC = 40x /140 or 2x / 7 OC = OB - OC = 3x / 7 Distance of the car at beginning of 2nd trip = 3*20 / 7 Distance of the car at beginning of 3rd trip = 32*20 / 72 Distance of the car at beginning of nth trip = 3n-1*20 / 7n-1 trips will go on till the distance is reduced to zero . this will be the case when n approaches to infinity .hence the fly make infinite number of turns. But in my view it is not possible as car will take only 30 minutes to reach the wall. Thus fly can't make infinite number of turns.