Author Topic: Bike math problem  (Read 4248 times)

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Builderboy

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Bike math problem
« on: December 07, 2011, 06:15:09 pm »
Two bicycles are spaced 100 meters apart and start riding towards each other at 1 meter per second.  At the same time, a fly on the front of one bike starts flying towards the other bike at 2 meters per second.  As soon as the fly reaches the second bike, it turns around and starts flying back towards the first bike.  The fly repeats this process as the bikes draw closer together, eventually turning around an infinite number of times.  But how far does the fly travel before the bikes finally collide?

parserp

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Re: Bike math problem
« Reply #1 on: December 07, 2011, 06:17:16 pm »
Spoiler For you really want to cheat and know?:
100 meters (just think about it)
« Last Edit: December 07, 2011, 06:19:56 pm by parser padwan »

epic7

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Re: Bike math problem
« Reply #2 on: December 07, 2011, 06:19:21 pm »
I have too much math to do already today to solve this

imo_inx

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Re: Bike math problem
« Reply #3 on: December 07, 2011, 06:19:58 pm »
If he flew infinite times, then infinity. of course.

Builderboy

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Re: Bike math problem
« Reply #4 on: December 07, 2011, 06:20:43 pm »
The sum of an infinite set of numbers is not necessarily infinite

jacobly

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Re: Bike math problem
« Reply #5 on: December 07, 2011, 06:26:21 pm »
100*(2/3)+100*(1/3)*(2/3)+...

∞       1 n  2    200   2
∑ (100·(-)  ·-) = --- ÷ - = 100
n=0      3    3     3    3

« Last Edit: December 07, 2011, 06:28:00 pm by jacobly »

Builderboy

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Re: Bike math problem
« Reply #6 on: December 07, 2011, 06:26:50 pm »
Well done!  You did it the hard way though

parserp

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Re: Bike math problem
« Reply #7 on: December 07, 2011, 06:27:17 pm »
100*(2/3)+100*(1/3)*(2/3)+...

∞       1 n  2    200   3
∑ (100·(-)  ·-) = --- · - = 100
n=0      3    3     3    2

oh no... I thought I wasn't at school...

epic7

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Re: Bike math problem
« Reply #8 on: December 07, 2011, 06:27:23 pm »
So... 100?

Builderboy

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Re: Bike math problem
« Reply #9 on: December 07, 2011, 06:29:33 pm »
Yep the answer is 100, and this can be derived quite easily without any sums of sequences.  The bikes travel 1M/S to close a distance of 50M,  This would take 50 seconds.  The fly travels a constant velocity of 2M/S regardless of direction, and it does so until the bikes meet each other, so 50 seconds.  If the fly travels at 2M/S for 50 seconds, that equates to 100M total

epic7

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Re: Bike math problem
« Reply #10 on: December 07, 2011, 06:29:49 pm »
Parser got it!

parserp

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Re: Bike math problem
« Reply #11 on: December 07, 2011, 06:30:21 pm »
+1 for me