# A.4.8.4 Two Pools

- Author:
- Katie Akesson, LeonMilewski

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.
Below 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.

How would the vertical values of the two graphs compare when the pools are full?

When each pool is being filled by one hose and at the same rate, should the two graphs have the same slope? Why or why not? If not, which graph has a greater slope?

How would the graph of the large pool change when one hose was moved from the small pool to the large pool? Would its slope increase, decrease, or stay the same?