document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=155897>Question 155897</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Working together, Sara and Heidi can milk the cows in 2 hours. If they work alone, it takes Heidi 3 hours longer than it takes Sarah. How long would it take Heidi to milk the cows alone?\r<BR>\n" );
document.write( "\n" );
document.write( "I know the answer is 6 I just don't know how to get it. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #114875 by </B><A HREF=/tutors/aboutme.mpl?userid=ptaylor><B>ptaylor(2198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ptaylor><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=ptaylor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=114875\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "OK.<BR>\n" );
document.write( "Let x=amount of time it takes Heidi to milk the cows alone<BR>\n" );
document.write( "Then Heidi can milk the cows at the rate of 1/x cows per hour<BR>\n" );
document.write( "Let y=amount of time it takes Sarah to milk the cows alone<BR>\n" );
document.write( "Then Sara can milk the cows at the rate of 1/y cows per hour<BR>\n" );
document.write( "Now we are basically told that Sarah and Heidi can milk the cows together at the rate of 1/2 of the cows per hour<BR>\n" );
document.write( "So, 1/x+1/y=1/2 multiply each term by 2xy<BR>\n" );
document.write( "2y+2x=xy---------------------------------------eq1\r<BR>\n" );
document.write( "\n" );
document.write( "Alone Heidi can milk the cows in x hours (1/x)*x=1 (all the cows)<BR>\n" );
document.write( "And alone, Sarah can milk the cows in y hours (1/y)*y=1 <BR>\n" );
document.write( "But we are also told that alone, it takes Heidi three hours longer than it takes Sarah, So:\r<BR>\n" );
document.write( "\n" );
document.write( "x=y+3---------------eq2\r<BR>\n" );
document.write( "\n" );
document.write( "substitute x=y+3 into eq1\r<BR>\n" );
document.write( "\n" );
document.write( "2x+2(y+3)=(y+3)*y  get rid of parens\r<BR>\n" );
document.write( "\n" );
document.write( "2y+2y+6=y^2+3y simplify<BR>\n" );
document.write( "4y+6=y^2+3y  sybtract 4y and also 6 from eahc side\r<BR>\n" );
document.write( "\n" );
document.write( "4y-4y+6-6=y^2+3y-4y-6  collect like terms\r<BR>\n" );
document.write( "\n" );
document.write( "0=y^2-y-6 ot<BR>\n" );
document.write( "y^2-y-6=0 quadratic in standard form and it can be factored<BR>\n" );
document.write( "(y-3)(y+2)=0<BR>\n" );
document.write( "y=3 hrs------------------------amount of time it takes Sarah to milk the cows<BR>\n" );
document.write( "(Note: we disregard the solution y=-2 for in this case time is positive)\r<BR>\n" );
document.write( "\n" );
document.write( "Substitute y=3 into eq1<BR>\n" );
document.write( "x=3+3 =6 hrs ---------------------amount of time it takes Heidi to milk the cows\r<BR>\n" );
document.write( "\n" );
document.write( "CK<BR>\n" );
document.write( "1/3 + 1/6 =1/2<BR>\n" );
document.write( "2/6 + 1/6=1/2<BR>\n" );
document.write( "1/2=1/2\r<BR>\n" );
document.write( "\n" );
document.write( "and<BR>\n" );
document.write( "6=3+3<BR>\n" );
document.write( "6=6\r<BR>\n" );
document.write( "\n" );
document.write( "Hope this helps-----ptaylor\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );