document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=937145>Question 937145</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Randy and Paul can do a piece of work in 10 days ;Randy and Guy can do it in 8 days ;Paul and Guy can do it in 12 days. How long will it take to each to do it alone ? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #570572 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=570572\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let R= amount of time it takes Randy to do the work alone<BR>\n" );
document.write( "Then Randy works at the rate of 1/R of the job per day<BR>\n" );
document.write( "Let P= amount of time it takes Paul to do the work alone<BR>\n" );
document.write( "Then Paul works at the rate of 1/P of the job per day<BR>\n" );
document.write( "Let G=amount of time it takes Guy to do the work alone<BR>\n" );
document.write( "Then Guy works at the rate of 1/G of the job per day<BR>\n" );
document.write( "Sooooo our equations to solve are:<BR>\n" );
document.write( "1/R+1/P=1/10---------------------eq1<BR>\n" );
document.write( "1/R+1/G=1/8------------------------eq2<BR>\n" );
document.write( "1/P+1/G=1/12--------------------------eq3\r<BR>\n" );
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document.write( "Subtract eq2 from eq1  and we get:<BR>\n" );
document.write( "1/P-1/G=(1/10)-(1/8)=(4/40)-(5/40)=-1/40   add this to eq3<BR>\n" );
document.write( "2/P=(1/12)-(1/40)=(10/120)-(3/120)=7/120<BR>\n" );
document.write( "2/P=7/120<BR>\n" );
document.write( "1/P=7/240 substitute this into eq1-----------------EQ1a<BR>\n" );
document.write( "1/R=(1/10)-(7/240)=(24/240)-(7/240)=17/240<BR>\n" );
document.write( "1/R=17/240  substitute this into eq2-----------------EQ2a<BR>\n" );
document.write( "17/240 + 1/G=1/8<BR>\n" );
document.write( "1/G=(1/8)-(17/240)=(30/240)-(17/240)=13/240<BR>\n" );
document.write( "1/G=13/240------------------------------------------EQ3a<BR>\n" );
document.write( "From eq2a: (you can divide these out but it's easier to work in fractions when checking your work)<BR>\n" );
document.write( "17R=240<BR>\n" );
document.write( "R=240/17 days<BR>\n" );
document.write( "From eq1a:<BR>\n" );
document.write( "7P=240<BR>\n" );
document.write( "P=240/7 days<BR>\n" );
document.write( "From eq3a:<BR>\n" );
document.write( "13G=240<BR>\n" );
document.write( "G=240/13 days<BR>\n" );
document.write( "CK<BR>\n" );
document.write( "Randy and Paul<BR>\n" );
document.write( "(17/240)+(7/240)=????1/10<BR>\n" );
document.write( "24/240=1/10<BR>\n" );
document.write( "1/10=1/10<BR>\n" );
document.write( "Randy and Guy<BR>\n" );
document.write( "(17/240)+(13/240)=????1/8<BR>\n" );
document.write( "30/240=1/8<BR>\n" );
document.write( "1/8=1/8<BR>\n" );
document.write( "Paul and Guy<BR>\n" );
document.write( "(7/240)+(13/240)=????1/12<BR>\n" );
document.write( "20/240=1/12<BR>\n" );
document.write( "1/12=1/12\r<BR>\n" );
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document.write( "Does this help?---ptaylor\r<BR>\n" );
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document.write( " </SPAN>\n" );
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