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
sher mohammad
b.tech, iit delhi