document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=132052>Question 132052</A>: <I><SPAN STYLE=\"word-break: break-all;\"> It takes Gary 1 hour to milk all the cows, and it takes Dana 1.5 hours. How long will it take them to do the job together? Please explain all the steps and models/equations used. Thanks so much. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #96432 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=96432\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x=amount of time it takes  Dana and Gary working together to milk all the cows.<BR>\n" );
document.write( "To start with, lets work in minutes on this problem:\r<BR>\n" );
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document.write( "Gary can milk 1/60 of the cows per minute<BR>\n" );
document.write( "Dana can milk 1/90 of the cows per minute\r<BR>\n" );
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document.write( "Together, they can milk 1/60 + 1/90 of the cows per minute which equals<BR>\n" );
document.write( "3/180+2/180 = 5/180=1/36 of the cows per minute\r<BR>\n" );
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document.write( "So our equation to solve is:\r<BR>\n" );
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document.write( "(1/36)*x=1(1 being one job or all the cows)  multiply both sides by 36\r<BR>\n" );
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document.write( "x=36 min---------------time it takes Dana and Gary working together to milk all the cows.\r<BR>\n" );
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document.write( "Now, we will go ahead and solve it without switching to minutes\r<BR>\n" );
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document.write( "Gary milks at the rate of all the cows (or 1 job) per hour<BR>\n" );
document.write( "Dana milks at the rate of 1/1.5 or 2/3 of the cows (2/3 job) per hour\r<BR>\n" );
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document.write( "Together they milk at the rate of 1 +2/3 of the cows per hour or\r<BR>\n" );
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document.write( "3/3+2/3=5/3 of the cows per hour so our equation to solve is (Note: this tells us that working together, they can milk more that all the cows per hour):\r<BR>\n" );
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document.write( "(5/3)*x=1(1 being one job or all the cows) multiply each side by 3\r<BR>\n" );
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document.write( "5x=3  divide both sides by 5<BR>\n" );
document.write( "x=3/5---- hour time it takes  Dana and Gary working together to milk all the cows.<BR>\n" );
document.write( "(note that 3/5 hr =(3/5)*60=36 min)\r<BR>\n" );
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document.write( "Hope this helps----ptaylor\r<BR>\n" );
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