Question

A trough is 2 feet wide and 8 feet long with a cross-section that is triangular (equilateral). Water is being pumped in at 2 gallons per minute. How fast is the depth rising when it is 3 inches deep? How fast is the depth rising when it is 6 inches deep? When the depth is 1 foot, the inflow rate changes. If it is rising at 1 foot per minute at that time, what is the new rate that water is being poured into the trough? [You’ll need to use the fact that 1 cubic foot is approximately 7.48 gallons.]