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Instantaneous rate of change - pool

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A swimming pool is 20 ft wide, 40 ft long, 3 ft deep at the shallow end, and 9 ft deep at its deepest point. If the pool is being filled at a rate of 0.8 ft^3/min, how fast is the water level rising when the depth at the deepest point is 5 ft?

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Solution Summary

This uses a swimming pool to show how to determine instantaneous rate of change.

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Please refer to the attached picture,
we need to know the speed of a increases.
the cross section of the pool is a echelon, but we only study the bottom part, ...

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