document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1120860>Question 1120860</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Ann goes swimming regularly she wants to improve her fitness, so she<BR>\n" );
document.write( "decides to swim 10 lengths in the first session and increase the number of<BR>\n" );
document.write( "lengths she swims by 2 every session. When she reaches 50 lengths in a<BR>\n" );
document.write( "session, she will not increase the number any further. If Ann asks her<BR>\n" );
document.write( "friend Joy to come swimming with her, Joy starts coming at Sue's 8th<BR>\n" );
document.write( "session, Joy starts to swim 15 lengths and increases the number of<BR>\n" );
document.write( "lengths by 5 each time. After how many of Joy's sessions does she swim<BR>\n" );
document.write( "the same number of lengths as Ann?<BR>\n" );
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document.write( "I will assume that \"Ann\" and \"Sue\" are supposed to be the same person....<br><BR>\n" );
document.write( "Joy starts swimming at Ann's 8th session.<br><BR>\n" );
document.write( "Ann starts doing 10 lengths and increases the number by 2 each session.  So in her 8th session, the number of lengths she swims is 10+7(2) = 24.<br><BR>\n" );
document.write( "In Joy's first session, she swims 15 lengths, and she increases that number by 5 each session.<br><BR>\n" );
document.write( "Let x be the number of Joy's sessions after her first (i.e., after Ann's 8th).<br><BR>\n" );
document.write( "The number of lengths Ann swims x sessions after Joy's first is 24+2x; the number Joy swims that same session is 15+5x.<br><BR>\n" );
document.write( "The number of lengths they swim will be the same when 24+2x = 15+5x.<br><BR>\n" );
document.write( "24+2x = 15+5x<BR>\n" );
document.write( "3x = 9<BR>\n" );
document.write( "x = 3<br><BR>\n" );
document.write( "It will be 3 sessions after her first (i.e., her 4th session) when Joy swims the same number of lengths as Ann.<br><PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "Ann's sessions:\r\n" );
document.write( "     session number  1   2   3   4   5   6   7   8   9  10  <b>11</b>  12...\r\n" );
document.write( "          lengths   10  12  14  16  18  20  22  24  26  28  <b>30</b>  32...\r\n" );
document.write( "Joy's sessions:\r\n" );
document.write( "     session number                              1   2   3   <b>4</b>   5...\r\n" );
document.write( "          lengths                               15  20  25  <b>30</b>  35...\r\n" );
document.write( "</PRE><br><BR>\n" );
document.write( "Of course, you could solve the problem without formal algebra, simply by writing out a table like the one shown.<BR>\n" );
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