document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=861017>Question 861017</A>: <I><SPAN STYLE=\"word-break: break-all;\"> It takes a small sprinkler 12 min longer to soak a lawn than it takes a large sprinkler. Working together, the sprinklers can soak the lawn in 8 min. How long would it take each sprinkler, working alone, to soak the lawn?<BR>\n" );
document.write( "small sprinkler    	  <BR>\n" );
document.write( "______<BR>\n" );
document.write( " min<BR>\n" );
document.write( "large sprinkler  ______ min.  	  \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 #518885 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=518885\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> It takes a small sprinkler 12 min longer to soak a lawn than it takes a large sprinkler.<BR>\n" );
document.write( " Working together, the sprinklers can soak the lawn in 8 min.<BR>\n" );
document.write( " How long would it take each sprinkler, working alone, to soak the lawn?<BR>\n" );
document.write( ":<BR>\n" );
document.write( "let t = time required by the larger sprinkler<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(t+12) = time required by the small<BR>\n" );
document.write( ":<BR>\n" );
document.write( "the completed job = 1 (a soaked lawn)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Each will do a fraction of the job, the two fractions add up to 1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2Ft ALIGN=MIDDLE  ALT=\"8%2Ft\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2F%28%28t%2B12%29%29 ALIGN=MIDDLE  ALT=\"8%2F%28%28t%2B12%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
document.write( "multiply by t(t+12) to clear the denominators, results:<BR>\n" );
document.write( "8(t+12) + 8t = t(t+12)<BR>\n" );
document.write( "8t + 96 + 8t = t^2 + 12t<BR>\n" );
document.write( "combine to form a quadratic on the right<BR>\n" );
document.write( "0 = t^2 + 12t - 16t - 96<BR>\n" );
document.write( "t^@ - 4t - 96 = 0<BR>\n" );
document.write( "Factors to<BR>\n" );
document.write( "(t-12)(t+8) = 0<BR>\n" );
document.write( "positive solution<BR>\n" );
document.write( "t = 12 min for the larger sprinkler<BR>\n" );
document.write( "and<BR>\n" );
document.write( "12 + 12 = 24 min for the small one\r<BR>\n" );
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