document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=472643>Question 472643</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 2.	Brenda jogs and walks a loop that is 6 km long for exercise every day. Her walking speed, on average, is 4 km/hour, while her jogging speed is 8 km/hour. On Tuesday, the entire loop took her 1 hour. Set up one equation using the total amount of time. Set up the other equation using distance = rate x time (actually in this case it’s distance = rate walking x time walking + rate jogging x time jogging).<BR>\n" );
document.write( "a.	Set up a system of equations to model this situation. How did you figure out what each equation would be? Let j = time spent jogging and w = time spent walking.<BR>\n" );
document.write( "b.	Solve this system of equations, showing all your work. <BR>\n" );
document.write( "c.	How much time did Brenda spend jogging on Tuesday?<BR>\n" );
document.write( "d.	How much time did Brenda spend walking on Tuesday?<BR>\n" );
document.write( "e.	How far, in km, did Brenda jog on Tuesday?<BR>\n" );
document.write( "f.	How far, in km, did Brenda walk on Tuesday?<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #324082 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=324082\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> brenda walks at 4 km/h.<BR>\n" );
document.write( "brenda jogs at 8 km/h.<BR>\n" );
document.write( "the loop is 6 km long.<BR>\n" );
document.write( "on tuesday, the total time it took to do the loop = 1 hour.<BR>\n" );
document.write( "j = amount of hours she spent jogging.<BR>\n" );
document.write( "w = amount of hours she spent walking.<BR>\n" );
document.write( "first equation is:<BR>\n" );
document.write( "j + w = 1<BR>\n" );
document.write( "let d1 = the distance she went walking.<BR>\n" );
document.write( "let d2 = the distance she went jogging.<BR>\n" );
document.write( "second equation is:<BR>\n" );
document.write( "d1 + d2 = 6<BR>\n" );
document.write( "the formula to use to solve this type of problem is:<BR>\n" );
document.write( "rate * time = distance<BR>\n" );
document.write( "for walking, we get:<BR>\n" );
document.write( "4 * w = d1<BR>\n" );
document.write( "for jogging, we get:<BR>\n" );
document.write( "8 * j = d2<BR>\n" );
document.write( "since we know that d1 + d2 = 6, then we add these equations together to get:<BR>\n" );
document.write( "4*w + 8*j = 6<BR>\n" );
document.write( "since we know that j + w = 1, we can solve for either one and use that to solve the equation for one of the variables.<BR>\n" );
document.write( "we'll use j = 1 - w.<BR>\n" );
document.write( "the equation of 4*w + 8*j = 6 becomes:<BR>\n" );
document.write( "4*w + 8*(1-w) = 6<BR>\n" );
document.write( "expand this to get:<BR>\n" );
document.write( "4*w + 8 - 8*w = 6<BR>\n" );
document.write( "subtract 8 from both sides of this equation to get:<BR>\n" );
document.write( "4*w - 8*w = -2<BR>\n" );
document.write( "combine like terms to get:\"<BR>\n" );
document.write( "-4*w = -2<BR>\n" );
document.write( "divide both sides of this equation by -4 to get:<BR>\n" );
document.write( "w = 2/4 = 1/2<BR>\n" );
document.write( "this means that j also equals 1/2 because j + w = 1<BR>\n" );
document.write( "this means that brenda walked for 1/2 hour and jogged for 1/2 hour.<BR>\n" );
document.write( "if she walked for 1/2 hour at 4 km/h then she walked for 2 km.<BR>\n" );
document.write( "if she jogged for 1/2 hour at 8 km/h then she jogged for 4 km.<BR>\n" );
document.write( "2 km + 4km = 6 km which is the distance of the loop.<BR>\n" );
document.write( "numbers check out.<BR>\n" );
document.write( "answers to your questions are:<BR>\n" );
document.write( "a.	Set up a system of equations to model this situation. How did you figure out what each equation would be? Let j = time spent jogging and w = time spent walking.<BR>\n" );
document.write( "see the work above.<BR>\n" );
document.write( "the system of equations that was used to solve the problem was:<BR>\n" );
document.write( "d1 + d2 = 6<BR>\n" );
document.write( "j + w = 1<BR>\n" );
document.write( "4*w = d1<BR>\n" );
document.write( "8*j = d2<BR>\n" );
document.write( "d1 was the walking distance in km.<BR>\n" );
document.write( "d2 was the jogging distance in km.<BR>\n" );
document.write( "w was the walking time in hours.<BR>\n" );
document.write( "j was the jogging time hours.<BR>\n" );
document.write( "4 was the walking rate of speed in km/h.<BR>\n" );
document.write( "8 was the jogging rate of speed in km/h.<BR>\n" );
document.write( "b.	Solve this system of equations, showing all your work.<BR>\n" );
document.write( "done. <BR>\n" );
document.write( "c.	How much time did Brenda spend jogging on Tuesday?<BR>\n" );
document.write( "1/2 hour.<BR>\n" );
document.write( "d.	How much time did Brenda spend walking on Tuesday?<BR>\n" );
document.write( "1/2 hour.<BR>\n" );
document.write( "e.	How far, in km, did Brenda jog on Tuesday?<BR>\n" );
document.write( "4 km.<BR>\n" );
document.write( "f.	How far, in km, did Brenda walk on Tuesday?<BR>\n" );
document.write( "2 km.\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( " </SPAN>\n" );
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