Question

There are two ponds of the same size. The first one has 1 water lily and the second has 2 lilies. Every 5 seconds, each lily in both ponds doubles itself. The first pond takes 5 minutes to fill. How much time will the second pond need?

Answer 1

Answer is: 4 minutes 55 seconds, but please explain the algebra.

Answer 2

okayy.. we know each 5 sec lily doubles..
5 min 300 secs
in this 300 secs the lily doubles itself 60 times.. the starting term is 1
so the seq goes on..
now what is this seq.. its just 2^n.
2^0=1
2^1=2
2^2=4
so on..
now 2^ 59=5.7 * 10^17 would be the amount of lilies required to fill the pond
assuming both ponds to be same in size.. when the number of lilies become 2^59 in pond 2.. its full
pond two starts with 2 lilies
ie 2^1.. this means that its 1 term ahead of pond 1.. thus pond 2 blossoms 5 secs before pond 1 :)