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December 18, 2014

December 18, 2014

Posted by **Confused!** on Thursday, April 19, 2012 at 4:57pm.

into the air and lands another mile from the stake (i.e., a total of two miles from the stake). The flea is undaunted and leaps into the air again, landing on the rubber band one inch further

along. Once again the giant kangaroo jumps another mile. The flea again leaps bravely into the air and lands another inch along the rubber band. If this continues indefinitely, will the flea

ever catch the kangaroo? (Assume the earth is flat and continues indefinitely in all directions.)

Okay so I tried this problem, and initially, I thought it was definitely a yes because every time the kangaroo jumps, the flea or whatever is dragged along with it. And eventually the flea will catch up the the kangaroo right? But then I tried it out in a Microsoft Excel document where

A is the #'s 1-100,

B is 5280*L1,

C is A/A*C+1 (i.e. C2 is A2/A1*C1+1 which is the ratio of the rubber band length before and after the kangaroo jumps [how much the flea is dragged along] plus the 1 inch that the flea jumps), and

D is B-C (for how far apart the flea and the kangaroo are)

The problem is, the difference between the flea and the kangaroo kept increasing and increasing so I have no idea what to do now. I know the answer is almost definitely yes... (otherwise what's the point of the problem?) but I can't get the math to work out! Is there a better way to prove it??

- Math -
**Steve**, Thursday, April 19, 2012 at 11:57pmLet the ratio of 1in/1mi be x

After each jump, we have the fraction of the distance of the flea from the roo:

1in/1mi

2in/2mi

3in/3mi

The flea is always 1/x of the way to the roo. He'll never make it.

- Math -
**Confused!**, Sunday, April 22, 2012 at 8:28amBut after each time the kangaroo jumps, the flea also jumps one inch so the ratio can't just be 1 in/1 mile

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