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.)
ok this one is PHUN
after the flea jumps on the rubberband, everytime the rubberband stretches the flea gets pulled along, as a rubberband stretches, part of it moves towards the object stretching it
Thus each time the roo jumps the flea is pulled along a little bit... Thus after it jumps, it really has moved an amount of the stretch plus the one inch
So yes it will catch the kangaroo after a long time because it will move the flea a little bit each time it jumps closer towards it, plus the one inch
SOLVED
It's not so fair to ask promys questions on here, now is it...
To answer this question, we need to consider the distances covered by both the kangaroo and the flea after each leap.
Let's break it down step by step:
1. After the first leap, the kangaroo is 1 mile away from the stake, whereas the flea is 1 inch away from the stake on the rubber band.
2. After the second leap, the kangaroo is now 2 miles away from the stake, and the flea has moved 1 inch along the rubber band.
3. After the third leap, the kangaroo is 3 miles away from the stake, and the flea has moved another inch along the rubber band.
And so on.
Based on this pattern, we can observe that for every mile the kangaroo jumps, the flea only moves an additional inch along the rubber band. This means that no matter how many times the kangaroo jumps, the distance between the kangaroo and the flea will always be increasing by a factor of 1 mile.
Since the flea is always lagging behind by an increasing distance, it will never be able to close the gap and catch up to the kangaroo.
Therefore, the flea will never catch the kangaroo as they will continue to move further apart with each leap.