# A.4.8.4 Two Pools

To prepare for a backyard party, a parent uses two identical hoses to fill a small pool that is 15 inches deep and a large pool that is 27 inches deep. The height of the water in each pool is a function of time since the water is turned on. Here are descriptions of three situations. For each situation, sketch the graphs of the two functions on the same coordinate plane, so that S(t) is the height of the water in the small pool after t minutes, and L(t) is the height of the water in the large pool after t minutes. In both functions, the height of the water is measured in inches. Situation 1: Each hose fills one pool at a constant rate. When the small pool is full, the water for that hose is shut off. The other hose keeps filling the larger pool until it is full. Situation 2: Each hose fills one pool at a constant rate. When the small pool is full, both hoses are shut off. Situation 3: Each hose fills one pool at a constant rate. When the small pool is full, both hoses are used to fill the large pool until it is full.