# Water Droplet Rings

**Algebra**Level 5

Please note that these rings are not consecutive as shown in the photo; there are other rings of varying radii in between each of the 6 rings.

Bobby soon realizes that there are infinitely many points in time where this can occur, so naturally the question arises: at what point in time does this first occur? If this time can be written in the form \(\frac{a}{b}\) where \(a\) and \(b\) are coprime positive integers, find \(a+b\).

**Details and Assumptions**:

Assume \(t=0\) as the point in which the first drop hits the water.

Note that the growth rate is in terms of the area of the circle, not the radius.

Circles of radius 0 are not considered circles.

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