document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=201997>Question 201997</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Respected sir,\r<BR>\n" );
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document.write( "plz help me to solve this arith problem...\r<BR>\n" );
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document.write( "1] Running at their respective constant rates, machine X takes 2 days longer to produce w widgets than machine Y. At these rates, if the two machines together produce 5/4 w widgets in 3 days, how many days would it take machine X alone to produce 2w widgets? \r<BR>\n" );
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document.write( "waiting for yurs reply sir.\r<BR>\n" );
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document.write( "Thank u.<BR>\n" );
document.write( "Regards<BR>\n" );
document.write( "Binita. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #152245 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=152245\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  Let x=amount of days it takes Y to produce w widgets<BR>\n" );
document.write( "Then Y produces at the rate of w/x widgets per day<BR>\n" );
document.write( "x+2=amount of days it takes X to produce w widgets<BR>\n" );
document.write( "Then X produces at the rate of w/(x+2) widgets per day<BR>\n" );
document.write( "Together the two machines work at the rate of w/x + w/(x+2)=(w(x+2)+wx)/x(x+2) widgets per day<BR>\n" );
document.write( "But we are told that the two machines together work at the rate of (5/12)w widgets per day ((5/4)w widgets in 3 days =(5/12)w widgets per day))\r<BR>\n" );
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document.write( "Now our first equation to solve is:<BR>\n" );
document.write( "(w(x+2)+wx)/x(x+2)=(5/12)w multiply each side by x(x+2)<BR>\n" );
document.write( "w(x+2)+wx=(5/12)wx(x+2) simplify<BR>\n" );
document.write( "wx+2w+wx=(5/12)wx^2+(10/12)wx<BR>\n" );
document.write( "2wx+2w=(5/12)wx^2+(10/12)wx multiply each term by 12<BR>\n" );
document.write( "24wx+24w=5wx^2+10wx subtract 24wx and 24w from each side<BR>\n" );
document.write( "5wx^2-14wx-24w=0  Assuming w is not equal to zero, divide each term by w<BR>\n" );
document.write( "5x^2-14x-24=0  quadratic in standard form<BR>\n" );
document.write( "If we use the quadratic formula to solve, we get:<BR>\n" );
document.write( "x=(14+-26)/10 or<BR>\n" );
document.write( "x=40/10=4---number of days it takes Y to produce w widgets<BR>\n" );
document.write( "and<BR>\n" );
document.write( "x=-14/10----Disregard.  Days in this problem are positive<BR>\n" );
document.write( "Now for X<BR>\n" );
document.write( "x+2=amount of days it takes X to produce w widgets or<BR>\n" );
document.write( "x+2=4+2=6----number of days it takes X to produce w widgets<BR>\n" );
document.write( "So X produces 2w widgets in 6*2=12 days--------------ans<BR>\n" );
document.write( "Another way to look at it: X produces at the rate of w/(x+2) widgets per day or<BR>\n" );
document.write( "w/(4+2)=w/6 widgets per day so in 12 days X produces (w/6)*12=2w widgets\r<BR>\n" );
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document.write( "Hope this helps---ptaylor\r<BR>\n" );
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document.write( " </SPAN>\n" );
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