Fly and cyclist

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

Correct answer:

x =  20 km
n = INF

Step-by-step explanation:

v1=10 km/h v2=20 km/h s=20 km  v2>v1 t1=s/(v1+v2)=20/(10+20)=320.6667 h s1=v2 t1=20 32=320 2=34013.3333 km  t2=(s2 t1 v1)/(v1+v2)=(202 32 10)/(10+20)=920.2222 h s2=v2 t2=20 92=920 2=9404.4444 km  t3=(s2 (t1+t2) v1)/(v1+v2)=(202 (32+92) 10)/(10+20)=2720.0741 h s3=v2 t3=20 272=2720 2=27401.4815 km  q1=t2/t1=92/32=92:32=92 23=9 22 3=186=310.3333 q2=t3/t2=272/92=272:92=272 29=27 22 9=5418=310.3333 q=q1=310.3333 a1=t1=320.6667  t = t1+t2+t3 +   t=1qa1=10.33330.6667=1 h  x=v2 t=20 1=20 km

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Showing 1 comment:
There is a much simpler way to find the distance that the fly travels: The two cyclists are 20 km apart, and are traveling at 10 km/hr. So they will meet in the middle after 1 hour. The fly is traveling at 20 km/hr, and does so for 1 hour before the cyclists meet. So the fly travels 20 km.

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