Fly and cyclist

Two cyclists are at 20 km apart on a same line. They start at same time towards each other at a speed of 10 km/hr. A fly sitting on one of the cyclists handle start flying towards the other cyclists at a speed of 20 km/hr. It touches the handle and move back to first one. Likewise it goes on till the two cyclists meet each other. What is the distance the fly travelled, and how many times it moved to and fro?

Result

x =  20 km
n = (Correct answer is: INF) Wrong answer

Solution:

v1=10 km/h v2=20 km/h s=20 km  v2>v1 t1=s/(v1+v2)=20/(10+20)=230.6667 h s1=v2 t1=20 0.6667=40313.3333 km  t2=(s2 t1 v1)/(v1+v2)=(202 0.6667 10)/(10+20)=290.2222 h s2=v2 t2=20 0.2222=4094.4444 km  t3=(s2 (t1+t2) v1)/(v1+v2)=(202 (0.6667+0.2222) 10)/(10+20)=2270.0741 h s3=v2 t3=20 0.0741=40271.4815 km  q1=t2/t1=0.2222/0.6667=130.3333 q2=t3/t2=0.0741/0.2222=130.3333 q=q1=0.3333=130.3333 a1=t1=0.6667=230.6667  t=t1+t2+t3+  t=a11q=0.666710.3333=1 h  x=v2 t=20 1=20 km
n=



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