document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=763148>Question 763148</A>: <I><SPAN STYLE=\"word-break: break-all;\"> man A set out from a certain point and travelled at the rate of 6 kph. After A had gone 2 hrs, another man B set out to overtake him and went 4km the 1st hour, 5km for the second hour, 6 km for the 3rd hour and so on gaining 1 km every hour. After how many hours will they be together?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #464651 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=464651\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> man A set out from a certain point and travelled at the rate of 6 kph.<BR>\n" );
document.write( " After A had gone 2 hrs, another man B set out to overtake him and<BR>\n" );
document.write( " went 4km the 1st hour, 5km for the second hour, 6 km for the 3rd hour<BR>\n" );
document.write( " and so on gaining 1 km every hour.<BR>\n" );
document.write( "After how many hours will they be together?<BR>\n" );
document.write( ";<BR>\n" );
document.write( "We know from the information given, that Man A has traveled 12 km when<BR>\n" );
document.write( "Man B starts after him.<BR>\n" );
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document.write( "Let x = no. of hrs for B to catch A<BR>\n" );
document.write( "x also = no. of km added to 4 km by the man B after x hrs<BR>\n" );
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document.write( "B's dist = A's dist<BR>\n" );
document.write( "x(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-1%29%2F2 ALIGN=MIDDLE  ALT=\"%28x-1%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >+4) = 6x + 12<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2-1x%29%2F2 ALIGN=MIDDLE  ALT=\"%28x%5E2-1x%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >+4x = 6x + 12<BR>\n" );
document.write( "multiply both sides by 2<BR>\n" );
document.write( "x^2 - x + 8x = 12x + 24<BR>\n" );
document.write( "combine like terms on the left<BR>\n" );
document.write( "x^2 - x + 8x - 12x - 24 = 0<BR>\n" );
document.write( "x^2 - 5x - 24 = 0<BR>\n" );
document.write( "Factors to:<BR>\n" );
document.write( "(x-8)(x+3) = 0<BR>\n" );
document.write( "The positive solution<BR>\n" );
document.write( "x = 8 hrs from the time B starts,they are together <BR>\n" );
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document.write( "Prove this by doing it the long way<BR>\n" );
document.write( "Hr_A___B (add one km each hr)<BR>\n" );
document.write( " 1  18 km, 4 km<BR>\n" );
document.write( " 2  24 km, 9 km, added 5<BR>\n" );
document.write( " 3  30 km, 15 km, added 6<BR>\n" );
document.write( " 4  36 km, 22 km, added 7<BR>\n" );
document.write( " 5  42 km, 30 km, added 8<BR>\n" );
document.write( " 6  48 km, 39 km, added 9<BR>\n" );
document.write( " 7  54 km, 49 km, added 10<BR>\n" );
document.write( " 8  60 km, 60 km, added 11, same distance after 8 hrs\r<BR>\n" );
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document.write( "  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );