document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=263015>Question 263015</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 5. Mary can clean an office complex in 5 hours.Working together John and Mary can clean the office complex in 3.5 hours.How long would it take John to clean the office complex by himself? \r<BR>\n" );
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document.write( "6. Working alone,Maria can complete a task in 100 minutes.Nora can complete the same task in two hours.They work together for thirty minutes when Cita,the new employee,joins and begin helping.They finished the task 20 minutes later.How long would it take Cita to complete the task alone?\r<BR>\n" );
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document.write( "                            thank u very very much!\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #193764 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><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=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=193764\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 5. Mary can clean an office complex in 5 hours.Working together John and Mary can clean the office complex in 3.5 hours.How long would it take John to clean the office complex by himself?<BR>\n" );
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document.write( "Let x = time it would take for John to clean office alone<BR>\n" );
document.write( "then<BR>\n" );
document.write( "3.5(1/5 + 1/x) = 1<BR>\n" );
document.write( "Multiplying both sides by 5x:<BR>\n" );
document.write( "3.5(x + 5) = 5x<BR>\n" );
document.write( "3.5x + 17.5 = 5x<BR>\n" );
document.write( "17.5 = 1.5x<BR>\n" );
document.write( "17.5/1.5 x<BR>\n" );
document.write( "175/15 = x<BR>\n" );
document.write( "35/3 = x<BR>\n" );
document.write( "11 2/3 hours = x<BR>\n" );
document.write( "or<BR>\n" );
document.write( "11 hours and 40 minutes = x\r<BR>\n" );
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document.write( "6. Working alone,Maria can complete a task in 100 minutes.Nora can complete the same task in two hours.They work together for thirty minutes when Cita,the new employee,joins and begin helping.They finished the task 20 minutes later.How long would it take Cita to complete the task alone? <BR>\n" );
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document.write( "First, convert the 2 hours into minutes:<BR>\n" );
document.write( "2*60 = 120 minutes<BR>\n" );
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document.write( "Let x = time it takes Cita to complete task alone<BR>\n" );
document.write( "then<BR>\n" );
document.write( "30(1/100 + 1/120) + 20(1/100 + 1/120 + 1/x) = 1<BR>\n" );
document.write( "Multiplying both sides by (100)(120)x:<BR>\n" );
document.write( "30(120x + 100x) + 20(120x + 100x + 12000) = 12000x<BR>\n" );
document.write( "Divide both sides by 10:<BR>\n" );
document.write( "3(120x + 100x) + 2(120x + 100x + 12000) = 1200x<BR>\n" );
document.write( "360x + 300x + 240x + 200x + 24000 = 1200x<BR>\n" );
document.write( "1100x + 24000 = 1200x<BR>\n" );
document.write( "24000 = 100x<BR>\n" );
document.write( "240 minutes = x<BR>\n" );
document.write( "or<BR>\n" );
document.write( "4 hours = x<BR>\n" );
document.write( "So Cita can do the task alone in 4 hours. </SPAN>\n" );
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