Related Rates Math Question

Question

A cubic box (6 inches in length) is filled with water in exactly in 3 minutes. How fast does the water level rise in a room measured to be 10 feet by 12 feet by 8 feet (LxWxH) the moment the water in the room is 5 feet deep.

Answer 1

V(cube) = x³

dV/dt = 6³/3 = 72 inches²/min = 3x² (dx/dt)

dx/dt = 72/(3*6²) = 2/3 inch/min

V(room) = l * w * h

dV/dt = l * w * (dh/dt) + (dl/dt) * w * h + l * (dw/dt) * h

dl/dt = dw/dt = 2/3 inch/min

72 = (10)(12)(dh/dt) + (2/3)(12)(5) + (10)(2/3)(5)

dh/dt = ?

The given information is not cleared if the room and the box are the same or if the water flow is flowing at the same rate. This is the solution I can figure out, let me know if you have any doubts and if this does not make sense. Thanks.