How SmaRT are You::The Famous Fly Puzzle

Discussion in 'Quiz | Puzzles | Mathematics' started by da_joker, May 30, 2012.

da_jokerCertified CEan

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Two bicyclists start twenty miles apart and head toward each other, each going at a steady rate of 10 mph. At the same time a fly that travels at a steady 15 mph starts from the front wheel of the southbound bicycle and flies to the front wheel of the northbound one, then turns around and flies to the front wheel of the southbound one again, and continues in this manner till he is crushed between the two front wheels. Question: what total distance did the fly cover?....

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In one hour with a speed of 15 mph, the fly should cover a total distance of 15 x 1 = 15 miles.
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ianoopStar

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what if fly speed is 25mph
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I'm not putting any more thought into this. Am I overlooking anything obvious?

da_jokerCertified CEan

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Big_K is right here....
The slow way to find the answer is to calculate what distance the fly covers on the first,
northbound, leg of the trip, then on the second, southbound, leg, then on the third, etc., etc., and,
finally, to sum the infinite series so obtained. The quick way is to observe that the bicycles meet......
exactly one hour after their start, so that the fly had just an hour for his travels; the answer must therefore be 15 miles.
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akash.kasinaCertified CEan

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i
i tried by summing all the terms in the infinite series and ended up in total confusion and some decimal value,good thinking dude!

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gwendollenCertified CEan

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ya its very simple logic............it is 15miles.............and if the fly sped is 25mph then the ans is 25 miles..........

ianoopStar

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Nope..if speed would be 25mph, then number of round taken by fly will be infinite.
since fly speed(25) > *bicycle relative speed (20).

gwendollenCertified CEan

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it means if the speed of the fly is 30mph then also the rounds taken by it will be infinte??????
i am not able to understand the logic in your answer..........plz explain it...........

Dilip jainCertified CEan

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itz not infinite.....it is the speed .........coz the fly just flies as long as the bicycles meet

ianoopStar

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I think you are right... had solved this type of question long ago.. didn't remembered the process.
but definitely number of round will be infinite.

Dilip jainCertified CEan

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hmm......i'll get back to u soonnnnn

gwendollenCertified CEan

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i agree with u.....

Dilip jainCertified CEan

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guys .........i can bet on it .....it is not "infinite"

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There is no way that I can see for an infinite loop unless the fly was superman and actually flew fast enough to turn back time...25 miles per hour for an hour would be 25 miles covered, excepting some really off the wall physics like surface curvature creating a difference between the distance flown and the actual distance of ground between marked axis of pivotal points.
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da_jokerCertified CEan

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guys it is not infinite....remember dey just have 1 hour to move..try to some the series together....u probably get 15.....

da_jokerCertified CEan

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.......

VassilyaCertified CEan

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Yeye, we've established the answer, we're debating variations now

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