A triangular horse troph is 3 feet long, 1 foot above the base, and 2 feet wide. There are two pipes, pipe A is at the top of the troph pouring in 3 gallons of water a minute, while pipe B is at the bottom of the troph, draining 4 gallons a minute. The water already in the troph is 9 inches high.
1. At what rate is the water draining when the water level is 6 inches above the base.
2. How long will it take for the water level to reach 6 inches above the base.
3. How long will it take for the troph to drain completely?
Very nice, Alan.....I like the way you set up the equation in terms of h and t
Here's a graph of the function that relates h and t.......https://www.desmos.com/calculator/1t8vmw70lp
Notice that when t = 7.013, h= 6.....and when t = 12.623, h =0......both confirm Alan's calculations
Also.....I have plotted the tangent line to the curve when t = 7.013.......this tangent line will have a slope of -77/144 ≈ -.5347.....indicating, as Alan has said, that the water level is falling at about .535 in/min when h = 6