Spring in Southern California has finally arrived. You are looking forward to filling your swimming pool, which has a length of 10 meters and ends with trapezoidal shape.

Spring in Southern California has finally arrived. You are looking forward to filling your swimming pool, which has a length of 10 meters and ends with trapezoidal shape. The trapezoids on the ends have a bottom edge with length 6 meters, a top edge with length 12 meters, and a height of 2 meters. Your hose can produce 3 cubic meters of water per hour. You begin to fill your pool. When the height of the water reaches 0.1 m, you realize this will take a long time. Calculate the rate the height of the water is increasing when it is 0.1 m high. Use this value to estimate how long it will take to fill the pool. Is this an overestimate or underestimate? Explain your reasoning.

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