document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=169575>Question 169575</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0321269470/algebrahomeworkh>Introductory Algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> A student walks and jogs to college each day. She averages 5 km/h walking and 9 km/h jogging. The distance from home to college is 8 km, and she makes the trip in 1 hr. How far does the student jog? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #124994 by </B><A HREF=/tutors/aboutme.mpl?userid=gonzo><B>gonzo(654)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gonzo><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=124994\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let W = rate of walking = 5 km/h<BR>\n" );
document.write( "let J = rate of jogging = 9 km/h<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "D = 8 km (given)<BR>\n" );
document.write( "T = 1 hour (given)<BR>\n" );
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document.write( "rate * time = distance.<BR>\n" );
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document.write( "let x = amount of time walking.<BR>\n" );
document.write( "let y = amount of time jogging.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "x * W = distance walking.<BR>\n" );
document.write( "y * J = distance jogging.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "since total time = 1 hour, then x + y = 1<BR>\n" );
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document.write( "since total distance = 8 km, then x*W + y*J = 8<BR>\n" );
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document.write( "you have 2 equations:<BR>\n" );
document.write( "x + y = 1<BR>\n" );
document.write( "x * W + y * J = 8<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "since W = 5 km/h and J = 9 km/h, then second equation becomes:<BR>\n" );
document.write( "x * 5 + y * 9 = 8<BR>\n" );
document.write( "which is the same as<BR>\n" );
document.write( "5x + 9y = 8<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "two equations become:<BR>\n" );
document.write( "x + y = 1<BR>\n" );
document.write( "5x + 9y = 8<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "if x + y = 1, then y = 1 - x<BR>\n" );
document.write( "second equation of 5x + 9y = 8 becomes:<BR>\n" );
document.write( "5x + 9*(1-x) = 8<BR>\n" );
document.write( "remove parentheses:<BR>\n" );
document.write( "5x + 9 - 9x = 8<BR>\n" );
document.write( "combine like terms:<BR>\n" );
document.write( "-4x + 9 = 8<BR>\n" );
document.write( "subtract 9 from both sides:<BR>\n" );
document.write( "-4x = -1<BR>\n" );
document.write( "divide both sides by 4:<BR>\n" );
document.write( "x = 1/4<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "if x = 1/4 and x + y = 1, then y = 3/4<BR>\n" );
document.write( "you have:<BR>\n" );
document.write( "x = 1/4 of an hour.<BR>\n" );
document.write( "y = 3/4 of an hour.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "you can now solve for distance since you have the rate and the time.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "equation to use is:<BR>\n" );
document.write( "5x + 9y = 8<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "5*x = 5 * 1/4 = 5/4 miles.<BR>\n" );
document.write( "9*y = 9 * 3/4 = 27/4 miles.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "she walked 5/4 miles.<BR>\n" );
document.write( "she jogged 27/4 miles.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "how does this work out?<BR>\n" );
document.write( "in the formula 5x + 9y = 8, we can substitute 1/4 for x since she walked 1 quarter of an hour, and we can susbtitute 3/4 for y since she jogged 3/4 of an hour.<BR>\n" );
document.write( "1/4 * 5 + 3/4 * 9 must equal 8<BR>\n" );
document.write( "5/4 + 27/4 = 32/4 = 8.<BR>\n" );
document.write( "since 8 = 8 the equation is true.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "student jogged 27/4 miles = 6.75 miles.<BR>\n" );
document.write( "she walked 5/4 miles = 1.25 miles.<BR>\n" );
document.write( "she jogged for 3/4 of an hour.<BR>\n" );
document.write( "she walked for 1/4 of an hour.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );