The tail of a giant kangaroo is attached by a giant rubber band to a stake in the ground. A
flea is sitting on top of the stake eyeing the kangaroo (hungrily). The kangaroo sees the flea
leaps into the air and lands one mile from the stake (with its tail still attached to the stake by
the rubber band). The flea does not give up the chase but leaps into the air and lands on the
stretched rubber band one inch from the stake. The giant kangaroo, seeing this, again leaps
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.)
Tigger, Thumper, Diamond, ... or whoever --
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writeacher, is there anyway i can contact you?
Now now
Easy! Piece of cake, buddy.
To answer this question, let's break down the distances and the situation step by step.
The kangaroo initially jumps one mile away from the stake while still being attached to it by the rubber band. The flea jumps one inch along the rubber band from the stake.
Now, when the kangaroo jumps another mile, it will be two miles away from the stake. Meanwhile, the flea jumps another inch along the rubber band. At this point, we can notice a pattern emerging.
For each mile the kangaroo jumps, the flea jumps one inch along the rubber band. So, as the kangaroo continues jumping, the flea will keep moving along the rubber band by the same proportion.
Since the kangaroo is leaping an entire mile each time, while the flea only jumps an inch along the rubber band, the flea will never be able to catch up with the kangaroo. The kangaroo will always be infinitely far away from the flea's position on the rubber band.
Therefore, no matter how many times they jump, the flea will never catch the kangaroo.