document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=598754>Question 598754</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1.'A' works twice as fast as 'B'. If both of them together take 6 days to complete the work, in how many days can 'B' alone complete the same?<BR>\n" );
document.write( "2.If 10 people working 8 hours a day, can complete a task in 24 days, how many people working 10 hours a day would be required to complete the same task in 16 days?<BR>\n" );
document.write( "3.’A’ alone can do a job in 25 days. He worked for 15 days and left. ‘B’ completed the remaining job in 10 days. If both of them work together after initial 15 days in how many more days would the job have been completed?<BR>\n" );
document.write( "4.If 10 men can complete a piece of work in 30 days how many men are requiredto complete the same job in 25 days?<BR>\n" );
document.write( "5.10men can complete a work in 18 days. After 6 days 5 more men joined. In how many days the remaining work would be completed? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #378689 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=378689\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (1)<BR>\n" );
document.write( "You add the individual rates of working to get<BR>\n" );
document.write( "the rate of working together<BR>\n" );
document.write( "Let A's rate = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+R%5Ba%5D+ ALIGN=MIDDLE  ALT=\"+R%5Ba%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Let B's rate  = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+R%7Bb%5D+ ALIGN=MIDDLE  ALT=\"+R%7Bb%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Working together their rate is ( 1 job ) / ( 6 days )<BR>\n" );
document.write( "given:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+R%5Ba%5D+=+2R%5Bb%5D+ ALIGN=MIDDLE  ALT=\"+R%5Ba%5D+=+2R%5Bb%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+R%5Ba%5D+%2B+R%5Bb%5D+=+1%2F6+ ALIGN=MIDDLE  ALT=\"+R%5Ba%5D+%2B+R%5Bb%5D+=+1%2F6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "By substitution:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2r%5Bb%5D+%2B+R%5Bb%5D+=+1%2F6+ ALIGN=MIDDLE  ALT=\"+2r%5Bb%5D+%2B+R%5Bb%5D+=+1%2F6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3R%5Bb%5D+=+1%2F6+ ALIGN=MIDDLE  ALT=\"+3R%5Bb%5D+=+1%2F6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+R%5Bb%5D+=+1%2F18+ ALIGN=MIDDLE  ALT=\"+R%5Bb%5D+=+1%2F18+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "B can finish the job in 18 days working alone<BR>\n" );
document.write( "check:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+R%5Ba%5D+=+2R%5Bb%5D+ ALIGN=MIDDLE  ALT=\"+R%5Ba%5D+=+2R%5Bb%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+R%5Ba%5D+=+2%2A%281%2F18%29+ ALIGN=MIDDLE  ALT=\"+R%5Ba%5D+=+2%2A%281%2F18%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+R%5Ba%5D+=+1%2F9+ ALIGN=MIDDLE  ALT=\"+R%5Ba%5D+=+1%2F9+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+R%5Ba%5D+%2B+R%5Bb%5D+=+1%2F6+ ALIGN=MIDDLE  ALT=\"+R%5Ba%5D+%2B+R%5Bb%5D+=+1%2F6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F9%5D+%2B+1%2F18%5D+=+1%2F6+ ALIGN=MIDDLE  ALT=\"+1%2F9%5D+%2B+1%2F18%5D+=+1%2F6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%2F18+%2B+1%2F18+=+3%2F18+ ALIGN=MIDDLE  ALT=\"+2%2F18+%2B+1%2F18+=+3%2F18+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3%2F18+=+3%2F18+ ALIGN=MIDDLE  ALT=\"+3%2F18+=+3%2F18+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OK<BR>\n" );
document.write( "---------<BR>\n" );
document.write( "(2)<BR>\n" );
document.write( "10 people working 8 hours a day, can complete a task in 24 days<BR>\n" );
document.write( "To finish in 1/3 of that time, each person works 3 times longer hours<BR>\n" );
document.write( "10 people working 24 hours a day take 8 days<BR>\n" );
document.write( "10 people working 12 hours a day take 16 days<BR>\n" );
document.write( "120 people working 1 hour a day take 16 days<BR>\n" );
document.write( "12 people working 10 hours a day take 16 days<BR>\n" );
document.write( "---------<BR>\n" );
document.write( "(3)<BR>\n" );
document.write( "What fraction of the job does A do in 15 days?<BR>\n" );
document.write( "His rate is ( 1 job ) / ( 25 days ), so<BR>\n" );
document.write( " fraction = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%281%2F25%29%2A15+=+3%2F5+ ALIGN=MIDDLE  ALT=\"+%281%2F25%29%2A15+=+3%2F5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "That means <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%2F5+ ALIGN=MIDDLE  ALT=\"+2%2F5+\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the job is left<BR>\n" );
document.write( "‘B’ completed the remaining job in 10 days<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+R%5Bb%5D+ ALIGN=MIDDLE  ALT=\"+R%5Bb%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = B's rate of working<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%2F5+=+R%5Bb%5D%2A10+ ALIGN=MIDDLE  ALT=\"+2%2F5+=+R%5Bb%5D%2A10+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+R%5Bb%5D+=+2%2F50+ ALIGN=MIDDLE  ALT=\"+R%5Bb%5D+=+2%2F50+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+R%5Bb%5D+=+1%2F25+ ALIGN=MIDDLE  ALT=\"+R%5Bb%5D+=+1%2F25+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "With both working together after the initial 15 days,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+R%5Ba%5D+%2B+R%5Bb%5D+ ALIGN=MIDDLE  ALT=\"+R%5Ba%5D+%2B+R%5Bb%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = rate woking together<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+R%5Ba%5D+%2B+R%5Bb%5D+=+1%2F25+%2B+1%2F25+ ALIGN=MIDDLE  ALT=\"+R%5Ba%5D+%2B+R%5Bb%5D+=+1%2F25+%2B+1%2F25+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+R%5Ba%5D+%2B+R%5Bb%5D+=+2%2F25+ ALIGN=MIDDLE  ALT=\"+R%5Ba%5D+%2B+R%5Bb%5D+=+2%2F25+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d ALIGN=MIDDLE  ALT=\"d\"   DISABLED_style= \"max-width:90%; height:auto;\" > = days to finish working together<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%2F5+=+%282%2F25%29%2Ad+ ALIGN=MIDDLE  ALT=\"+2%2F5+=+%282%2F25%29%2Ad+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d+=+%2825%2F2%29%2A%282%2F5%29+ ALIGN=MIDDLE  ALT=\"+d+=+%2825%2F2%29%2A%282%2F5%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d+=+5+ ALIGN=MIDDLE  ALT=\"+d+=+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The job will be completed in 5 more days or 20 days altogether<BR>\n" );
document.write( "------------<BR>\n" );
document.write( "(4)<BR>\n" );
document.write( "If 10 men take 30 days,<BR>\n" );
document.write( "then 60 men take 5 days<BR>\n" );
document.write( "then 12 men take 25 days<BR>\n" );
document.write( "( 1/5 as many men take 5 times longer )<BR>\n" );
document.write( "------------<BR>\n" );
document.write( "(5)<BR>\n" );
document.write( "10men can complete a work in 18 days<BR>\n" );
document.write( "In 1/3 of that time, 1/3 of the job gets done<BR>\n" );
document.write( "so, after 6 days, 2/3 of the job is left<BR>\n" );
document.write( "Now 5 men must do 2/3 of the job <BR>\n" );
document.write( "If 10men can complete a work in 18 days,<BR>\n" );
document.write( "5 men take 36 days to the job<BR>\n" );
document.write( "To do 2/3 of a job,<BR>\n" );
document.write( "number of days = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%282%2F3%29%2A36+=+24+ ALIGN=MIDDLE  ALT=\"+%282%2F3%29%2A36+=+24+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The remaining work is completed in 24 days<BR>\n" );
document.write( "------------\r<BR>\n" );
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document.write( "\n" );
document.write( " <BR>\n" );
document.write( "  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );