MathDB

The city of Atlantis is built on an island represented by

[ -1, 1]

, with skyline initially given by

f(x) = 1 - |x|

. The sea level is currently

y=0

, but due to global warming, it is rising at a rate of

0.01

a year. For any position

-1 < x < 1

, while the building at

x

is not completely submerged, then it is instantaneously being built upward at a rate of

r

per year, where

r

is the distance (along the

x

-axis) from this building to the nearest completely submerged building. How long will it be until Atlantis becomes completely submerged?
Proposed by Ethan Tan

Problem Statement