document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=98649>Question 98649</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A hose can fill a swimming pool in 6 hours. Another hose needs 3 more hours to fill the pool than the two hoses combined. How long would it take the second hose to fill the pool? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #71791 by </B><A HREF=/tutors/aboutme.mpl?userid=malakumar_kos@yahoo.com><B>malakumar_kos@yahoo.com(315)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=malakumar_kos@yahoo.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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=71791\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "     A hose can fill a swimming pool in 6 hours. Another hose needs 3 more hours to fill the pool than the two hoses combined. How long would it take the second hose to fill the pool?\r<BR>\n" );
document.write( "\n" );
document.write( "     let the two horses be A & B  \r<BR>\n" );
document.write( "\n" );
document.write( "         time taken by horse A = 6 hrs\r<BR>\n" );
document.write( "\n" );
document.write( "         time taken by horse B = y hrs\r<BR>\n" );
document.write( "\n" );
document.write( "         time taken by A & B together = 6+x  hrs \r<BR>\n" );
document.write( "\n" );
document.write( "                            y = 6+x+3 <BR>\n" );
document.write( "                            y = x+9...........(1)\r<BR>\n" );
document.write( "\n" );
document.write( "          Qu'ty of pool filled by A in 1 hr = 1/6\r<BR>\n" );
document.write( "\n" );
document.write( "          Qu'ty of pool filled by B in 1 hr = 1/y\r<BR>\n" );
document.write( "\n" );
document.write( "          Qu'ty  of pool filled by A & B in 1 hr = 1/(6+x) \r<BR>\n" );
document.write( "\n" );
document.write( "                               1/(6+x) = 1/6+1/y\r<BR>\n" );
document.write( "\n" );
document.write( "                               1/(6+x) = y+6/6y\r<BR>\n" );
document.write( "\n" );
document.write( "                                 6y = (6+y)(6+x)\r<BR>\n" );
document.write( "\n" );
document.write( "                                  6y = 36+6x+6y+xy\r<BR>\n" );
document.write( "\n" );
document.write( "                               -6x-xy = 36.......(2)\r<BR>\n" );
document.write( "\n" );
document.write( "      substituting for y in (2)  we get -6x - x(x+9)= 36\r<BR>\n" );
document.write( "\n" );
document.write( "                                        -6x -x^2-9x = 36\r<BR>\n" );
document.write( "\n" );
document.write( "                                        -x^2-15x-36 = 0\r<BR>\n" );
document.write( "\n" );
document.write( "                                          x^2+15x+36 =0<BR>\n" );
document.write( "      Factors of 36 are 12 &3            x^2+12x+3x+36 = 0\r<BR>\n" );
document.write( "\n" );
document.write( "                                         x(x+12)+3(x+12)= 0\r<BR>\n" );
document.write( "\n" );
document.write( "                                           (x+12)(x+3) = 0\r<BR>\n" );
document.write( "\n" );
document.write( "                                            x+12 = 0  or x = -12\r<BR>\n" );
document.write( "\n" );
document.write( "                                            x+3 = 0   or x = -3\r<BR>\n" );
document.write( "\n" );
document.write( "            time taken by horse B to fill the pool = y = x+9<BR>\n" );
document.write( "                                     if x = -3 then  y = -3+9 = 6 hrs<BR>\n" );
document.write( "                                     if x = -12 then y = -12+9 = -3 \r<BR>\n" );
document.write( "\n" );
document.write( "                 -3 hrs cannot be considered so  x= 6 hrs is the required value\r<BR>\n" );
document.write( "\n" );
document.write( "          </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );