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Question 1105016: 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?
Answer by greenestamps(13216)   (Show Source):
You can put this solution on YOUR website!
In fact, the expression you show has no meaning related to the problem:
The correct expression is
The average gallons per minute is the total number of gallons divided by the total number of minutes.
That means the denominator "2x+3" is the total number of minutes.
So the "x" and "x+3" in the numerator are the numbers of minutes that one hose and then two hoses were being used.
So the "2" and "6" in the numerator are the numbers of gallons per minute when one hose and when 2 hoses were being used.
Since obviously there would be more gallons per minute when two hoses are being used, there must have been one hose at 2 gallons per minute for x minutes, for a total number of gallons "2x", followed by two hoses at 6 gallons per minute (which means the second hose filled the pool at a rate of 4 gallons per minute) for (x+3) minutes, for a total of "6(x+3)" gallons.
So the parts of the expression are...
"2" -- gallons per minute for the first hose
"x" -- number of minutes the first hose alone was being used
"2x" -- number of gallons added by the first hose, before the second hose was added
"6" -- gallons per minute with both hoses together
"x+3" -- number of minutes both hoses were being used
"6(x+3)" -- number of gallons added when both hoses were working together
"2x+6(x+3)" --total number of gallons added
"2x+3" -- total time
"(2x+6(x+3))/(2x+3)" -- total gallons divided by total time; i.e., average gallons per minute
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