A container has a square bottom, a open square top, and four congruent trapezoidal sides, as shown. Starting when the container is empty, a hose that runs water at a constant rate takes minutes to fill the container up to the midline of the trapezoids.
How many more minutes will it take to fill the remainder of the container?
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Problem © Mathematical Association of America (MAA), American Mathematics Competitions. Reproduced for non-commercial educational use. Solution and commentary are original to this site.