Question

Arielle is filling up the kiddie pool for her younger sister and places a hose in the pool, allowing water to fill the pool. After a certain number of minutes, Arielle finds a second hose, places it in the kiddie pool, and allows more water to fill the pool.

Arielle can express the average rate of water entering the kiddie pool in gallons per minute as 2x+6(x+3)/2x+3.

What is the meaning of the parts of this rational expression in the context of the situation?

Select from the drop-down menus to correctly complete the statements.

The numerator of the rational expression represents the ____

The denominator of the rational expression represents the ____

Possible solutions for the fill in the blank above:
A. Total number of gallons of water in the kiddie pool.
B. Total number of minutes filling the kiddie pool.
C. Number of gallons each hose dispenses.

Answer 1

The given rational function that gives the average rate of water entering

the pool is the total volume in the pool divided by the time.

Response:

The numerator of the rational expression represents the;

A. Total number of gallons of water in the kiddie pool

The denominator of the rational expression represents the;

B. Total number of minutes of filling the kiddie pool

Which methods are used to determine the parts of the rational function?

The given parameters are;

$Expression \ for \ average \rate \ of \ water \ entering \ the \ pool = \mathbf{ \dfrac{2 \cdot x + 6 \cdot (x + 3)}{2 \cdot x + 3}}$

The parts of the given expression can be analyzed as follows;

x = The time in which the second hose is in use

2 = The flow rate of the second hose in gallons per minute

6 = The flow rate of the first hose in gallons per minute

x + 3 = The time in which the first hose is in use

x + x + 3 = 2·x + 3 = The total number of minutes of filling the kiddie pool

Therefore;

2·x = The volume added to the pool due to the second hose

6·(x + 3) = The volume added to the pool due to the first hose

2·x + 6·(x + 3) = Total number of gallons of water in the kiddie pool

Which gives;

The numerator of the rational expression represents the;

A. Total number of gallons of water in the kiddie pool

The denominator of the rational expression represents the;

B. Total number of minutes of filling the kiddie pool

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