document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1105016>Question 1105016</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 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.\r<BR>\n" );
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document.write( "Arielle can express the average rate of water entering the kiddie pool in gallons per minute as 2x+6(x+3)/2x+3 <BR>\n" );
document.write( "What is the meaning of the parts of this rational expression in the context of the situation? </SPAN>\n" );
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document.write( "In fact, the expression you show has no meaning related to the problem:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B6%28x%2B3%29%2F2x%2B3 ALIGN=MIDDLE  ALT=\"2x%2B6%28x%2B3%29%2F2x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The correct expression is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%2B6%28x%2B3%29%29%2F%282x%2B3%29 ALIGN=MIDDLE  ALT=\"%282x%2B6%28x%2B3%29%29%2F%282x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The average gallons per minute is the total number of gallons divided by the total number of minutes.<BR>\n" );
document.write( "That means the denominator \"2x+3\" is the total number of minutes.<BR>\n" );
document.write( "So the \"x\" and \"x+3\" in the numerator are the numbers of minutes that one hose and then two hoses were being used.<BR>\n" );
document.write( "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.<BR>\n" );
document.write( "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.<br><BR>\n" );
document.write( "So the parts of the expression are...<BR>\n" );
document.write( "\"2\" -- gallons per minute for the first hose<BR>\n" );
document.write( "\"x\" -- number of minutes the first hose alone was being used<BR>\n" );
document.write( "\"2x\" -- number of gallons added by the first hose, before the second hose was added<BR>\n" );
document.write( "\"6\" -- gallons per minute with both hoses together<BR>\n" );
document.write( "\"x+3\" -- number of minutes both hoses were being used<BR>\n" );
document.write( "\"6(x+3)\" -- number of gallons added when both hoses were working together<BR>\n" );
document.write( "\"2x+6(x+3)\" --total number of gallons added<BR>\n" );
document.write( "\"2x+3\" -- total time<BR>\n" );
document.write( "\"(2x+6(x+3))/(2x+3)\" -- total gallons divided by total time; i.e., average gallons per minute </SPAN>\n" );
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