A major river is divided into three parts or courses-the upper course, the middle course, and the

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A major river is divided into three parts or courses-the upper course, the middle course, and the lower course. The slope is \(70 \mathrm{ft}\) per mile in the upper course, \(10 \mathrm{ft}\) per mile in the middle course, and \(1.0 \mathrm{ft}\) per mile in the lower course. All three courses have rectangular cross sections. The upper course has a normal depth of \(40.0 \mathrm{ft}\). The river width is \(120 \mathrm{ft}\). Find the normal depths of the middle and lower courses.

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