document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1164424>Question 1164424</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Jim began a ​206-mile bicycle trip to build up stamina for a triathlete competition.​ Unfortunately, his bicycle chain​ broke, so he finished the trip walking. The whole trip took 6 hours. If Jim walks at a rate of 5 miles per hour and rides at 37 miles per​ hour, find the amount of time he spent on the bicycle. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #788823 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=788823\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> r * t = d<BR>\n" );
document.write( "r = rate<BR>\n" );
document.write( "t = time<BR>\n" );
document.write( "d = distance\r<BR>\n" );
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document.write( "walking is at 5 miles per hour.<BR>\n" );
document.write( "bicycling is at 37 miles per hour.\r<BR>\n" );
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document.write( "total distance is 206.<BR>\n" );
document.write( "total time is 6 hours.\r<BR>\n" );
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document.write( "lex x = time walking and let y = time riding the bicycle.\r<BR>\n" );
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document.write( "you get:\r<BR>\n" );
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document.write( "x + y = 6<BR>\n" );
document.write( "5x + 37y = 206\r<BR>\n" );
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document.write( "x + y is the total time.<BR>\n" );
document.write( "5x + 37y is the total distance<BR>\n" );
document.write( "in the second equation:<BR>\n" );
document.write( "5 is the rate and x is the time.<BR>\n" );
document.write( "37 is the rate and y is the time.\r<BR>\n" );
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document.write( "you have two equations that need to be solved simultaneously.<BR>\n" );
document.write( "they are:<BR>\n" );
document.write( "x + y = 6<BR>\n" );
document.write( "5x + 37y = 206\r<BR>\n" );
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document.write( "multiply both sides of the first equation by 5 and leave the second equation as is to get:\r<BR>\n" );
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document.write( "5x + 5y = 30<BR>\n" );
document.write( "5x + 37y = 206\r<BR>\n" );
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document.write( "subtract the first equation from the second to get:<BR>\n" );
document.write( "32y = 176<BR>\n" );
document.write( "solve for y to get:<BR>\n" );
document.write( "y = 5.5<BR>\n" );
document.write( "this makes x = .5 because x + y = 6\r<BR>\n" );
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document.write( "replace x and y with .5 and 5.5 in the original equations to get:<BR>\n" );
document.write( "x + y = 6 becomes .5 + 5.5 = 6 which is true.<BR>\n" );
document.write( "5x + 37y = 206 becomes 5 * .5 + 37 * 5.5 = 206 which becomes 2.5 + 203.5 = 206 which is also true.\r<BR>\n" );
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document.write( "x = .5 and y = 5.5 is confirmed to be good.<BR>\n" );
document.write( "solution is that he rode the bicycle for 5.5 hours.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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