document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1151536>Question 1151536</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this question: Machine A can do a piece of work in 6hrs while machine B can do the same work in 9hrs. Machine A and B was set to do the piece of work but after three and a half hours Machine A broke down. For how long machine B took to do the rest of the work </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #773309 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=773309\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A does the job in 6 hours.<BR>\n" );
document.write( "B does the job in 9 hours.\r<BR>\n" );
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document.write( "r * t = q<BR>\n" );
document.write( "r is the rate<BR>\n" );
document.write( "t is the time<BR>\n" );
document.write( "q is the quantity\r<BR>\n" );
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document.write( "in this problem q = 1 which represents one piece of work.\r<BR>\n" );
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document.write( "for machine A, the formula becomes r * 6 = 1<BR>\n" );
document.write( "solve for r to get r = 1/6\r<BR>\n" );
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document.write( "for machine B, the formula becomes r * 9 = 1<BR>\n" );
document.write( "solve for r to get r = 1/9\r<BR>\n" );
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document.write( "when they work together, their rates are additive.\r<BR>\n" );
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document.write( "the formula becomes (rA + rB) * t = q\r<BR>\n" );
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document.write( "they both work together for 3.5 hours.\r<BR>\n" );
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document.write( "the formula becomes (rA + rB) * 3.5 = q\r<BR>\n" );
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document.write( "since rA = 1/6 and rB = 1/9, the formula becomes (1/6 + 1/9) * 3.5 = q\r<BR>\n" );
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document.write( "solve for q to get q = (1/6 + 1/9) * 3.5 = (3/18 + 2/18) * 3.5 = 5/18 * 3.5 = 17.5/18 = 35/36.\r<BR>\n" );
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document.write( "when they worked together for 3.5 hours, they were able to complete 35/36 of the job.\r<BR>\n" );
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document.write( "that means that 1/36 of the job is left to do.\r<BR>\n" );
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document.write( "machine A broke down and machine B is left to finish the job.\r<BR>\n" );
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document.write( "formula for machine B to finish the job is equal to r * t = q which becomes 1/9 * t = 1/36\r<BR>\n" );
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document.write( "solve for t to get t = 9/36 hours = 1/4  hours = 15 minutes.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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