document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=511722>Question 511722</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Three bulldozer operators R, S and T can level off an area for a landing strip in 30 hours. R can do twice as much as S, and S can do 5/3 as much as T. How long would it take each to do 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 #342382 by </B><A HREF=/tutors/aboutme.mpl?userid=oberobic><B>oberobic(2304)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=oberobic><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=342382\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Problems like these are fraction problems.<BR>\n" );
document.write( "R does 1/R of the job per hr.<BR>\n" );
document.write( "S does 1/S of the job per hr.<BR>\n" );
document.write( "T does 1/T of the job per hr.<BR>\n" );
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document.write( "(1/R per hr + 1/S per hr + 1/T per hr) * 30 hr = 1 whole job<BR>\n" );
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document.write( "With three unknowns and one equation, which you cannot solve the problem.<BR>\n" );
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document.write( "But we're given some relationships.<BR>\n" );
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document.write( "R can do twice as much as S:<BR>\n" );
document.write( "1/R = 2 * 1/S = 2/S<BR>\n" );
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document.write( "S can do 5/3 as much as T:<BR>\n" );
document.write( "1/S = (5/3)*(1/T) = 5/(3T)<BR>\n" );
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document.write( "This means R can do 10/3 as much as T<BR>\n" );
document.write( "1/R = 2/S = 10/(3T)<BR>\n" );
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document.write( "(10/3T + 5/3T + 1/T)* 30 = 1<BR>\n" );
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document.write( "Multiply by 3T to eliminate fraction<BR>\n" );
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document.write( "(10 + 5 + 3)*30 = 3T<BR>\n" );
document.write( "(18)*30 = 3T<BR>\n" );
document.write( "3T = 540<BR>\n" );
document.write( "T = 180<BR>\n" );
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document.write( "T can do the job working alone in 180 hr<BR>\n" );
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document.write( "1/S = 5/(3T)<BR>\n" );
document.write( "cross multiply<BR>\n" );
document.write( "3T = 5S<BR>\n" );
document.write( "3(180) = 5S<BR>\n" );
document.write( "5S = 540<BR>\n" );
document.write( "S = 108<BR>\n" );
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document.write( "S can do the job in 108 hr<BR>\n" );
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document.write( "1/R = 2/S<BR>\n" );
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document.write( "1/R = 2/108<BR>\n" );
document.write( "cross multiply<BR>\n" );
document.write( "2R = 108<BR>\n" );
document.write( "R = 54<BR>\n" );
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document.write( "R can do the job in 54 hr<BR>\n" );
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document.write( "Check so see if they can the whole job in 30 hrs.<BR>\n" );
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document.write( "(1/R + 1/S + 1/T) * 30 = 1 ??<BR>\n" );
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document.write( "(1/54 + 1/108 + 1/180) * 30 = (10/540 + 5/540 + 3/540) * 30<BR>\n" );
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document.write( "(10/540 + 5/540 + 3/540) * 30 = (18/540) * 30<BR>\n" );
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document.write( "(18/540) * 30 = 540/540  = 1<BR>\n" );
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document.write( "Correct.<BR>\n" );
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document.write( "Answer: Working alone:<BR>\n" );
document.write( "R can do the whole job in 54 hr,<BR>\n" );
document.write( "S can do the whole job in 108 hr, and<BR>\n" );
document.write( "T can do the whole job in 180 hr.<BR>\n" );
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document.write( "Done. </SPAN>\n" );
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