SOLUTION: 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 seco

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
RELATED QUESTIONS
Chris is planning to fill up a kiddie swimming pool for his younger sister but he does... (answered by Alan3354)

If a basketball has a radius of 6 inches, approximately how many cubic inches of air will (answered by josgarithmetic)

Jimmy is filling up a pool using a large hose and a small hose. The large hose, working... (answered by macston)

Anita is filling a small pool for her kids. Currently, there are 60 gallons of water in... (answered by josmiceli)

Anita is filling a small pool for her kids currently there is 60 gallons of water in the... (answered by addingup)

hi :) i need help with this question - A water hose is being used to fill a kiddie... (answered by ankor@dixie-net.com)

A hose can fill a pool in 12 hours. A drainage pipe can empty the pool in 18 hours. If... (answered by ptaylor)

Isabella filled her pool with water at a constant rate. The table compares the remaining (answered by ikleyn)

Mary wants to fill a swimming pool that holds 15,000 gallons of water. if she fills from... (answered by ikleyn,amalm06)