# Two cyclists began a training run simultaneously, one starting from Pune, the other from Mumbai. When the riders were 150 Km apart, a fly took an interest. Starting on one cyclist’s shoulder, the fly flew ahead to meet the other cyclist. On reaching the latter, fly at once turned back. The restless fly continued to shuttle back and forth until the pair met; then it settle on the nose of one of the cyclists.The fly’s speed was 30 Km per hour. Each cyclist’s speed was 15 Km per hour. How many km did the fly travel?

10 years ago
the fly the relative speed of fly every time it approaches with double speed, let
distance covered by runner is x1, then by fly is 2x1, 3x1=150, 2x1=2*150/3
distance covered by runner is x2, then by fly is 2x2, 3x2=100, 2x2=2*150/9 and so on
the sum becomes 2*150/3(1+1/3+1/9+1/27.....)= 2*50/(1-1/3)=2*50*3/2=150

b.tech, iit delhi

God Of Maths
29 Points
9 years ago
Time Taken By The cyclists to meet is
Time = Distance / Total Speed
= 150/15+15
= 150/30
= 5 hrs
Speed of the fly was 30km/hr
Therefore distance traveled by the fly in 5hrs is
distance = speed * time
= 30 * 5
= 150 km
Therefore the fly travelled 150 km

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God of Maths