document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1177723>Question 1177723</A>: <I><SPAN STYLE=\"word-break: break-all;\"> It takes pump A 2 hours less time than pump B to empty a pool. Pump A is started at 8:00am and pump B at 10:00am. At 12:00pm 60% of the pool.is empty when pump B broke down. How much time after 12:00pm would it take pump A to empty the pool? </SPAN>\n" );
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document.write( "let x = # hours A takes alone to empty the pool<BR>\n" );
document.write( "then x+2 = # hours B takes alone<br><BR>\n" );
document.write( "1/x = fraction of job A does in 1 hour<BR>\n" );
document.write( "1(x+2) = fraction of job B does in 1 hour<br><BR>\n" );
document.write( "At 12pm when pump B broke down, A has been working 4 hours and B 2 hours.  The fraction of the job done at that time is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%281%2Fx%29%2B2%281%2F%28x%2B2%29%29 ALIGN=MIDDLE  ALT=\"4%281%2Fx%29%2B2%281%2F%28x%2B2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "That fraction of the job done at 12pm is 60% = 3/5. Solve that equation to find out how many hours A takes to empty the pool alone.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%281%2Fx%29%2B2%281%2F%28x%2B2%29%29+=+3%2F5 ALIGN=MIDDLE  ALT=\"4%281%2Fx%29%2B2%281%2F%28x%2B2%29%29+=+3%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Multiply through by the least common denominator <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%28x%29%28x%2B2%29 ALIGN=MIDDLE  ALT=\"5%28x%29%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20%28x%2B2%29%2B10%28x%29=3%28x%29%28x%2B2%29 ALIGN=MIDDLE  ALT=\"20%28x%2B2%29%2B10%28x%29=3%28x%29%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30x%2B40+=+3x%5E2%2B6x ALIGN=MIDDLE  ALT=\"30x%2B40+=+3x%5E2%2B6x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2-24x-40+=+0 ALIGN=MIDDLE  ALT=\"3x%5E2-24x-40+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "This does not factor; use the quadratic formula and of course use the positive root.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2824%2Bsqrt%281056%29%29%2F6 ALIGN=MIDDLE  ALT=\"x+=+%2824%2Bsqrt%281056%29%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 9.416 to 3 decimal places.<br><BR>\n" );
document.write( "2/5 of the pool remains to be emptied; the number of hours it will take A to finish is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9.416%2A0.4+=+3.7664 ALIGN=MIDDLE  ALT=\"9.416%2A0.4+=+3.7664\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER: to a few decimal places, 3.7664 hours<br>\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
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