document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1140236>Question 1140236</A>: <I><SPAN STYLE=\"word-break: break-all;\"> You travel the first 48 miles of a journey at an average of 36 mph and the second 48 miles at an average of v mph. What must be v if you want to average 45 mph over the 96 mile journey?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #760727 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=760727\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> r * t = d\r<BR>\n" );
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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( "for the first 48 miles, the equation becomes r1 * t1 = 48<BR>\n" );
document.write( "for the second 48 miles, the equation becomes r2 * t2 = 48\r<BR>\n" );
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document.write( "since r1 = 36, the first equation becomes 36 * t1 = 48<BR>\n" );
document.write( "solve for t1 to get t1 = 48/36\r<BR>\n" );
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document.write( "since r2 = v, the second equation becomes v * t2 = 48\r<BR>\n" );
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document.write( "for the overall trip, r * t = 96<BR>\n" );
document.write( "r is the overall rate<BR>\n" );
document.write( "t is the overall time\r<BR>\n" );
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document.write( "since r = 45, then r * t = 96 becomes 45 * t = 96.<BR>\n" );
document.write( "solve for t to get t = 96/45\r<BR>\n" );
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document.write( "since t1 + t2 = t, you get 48/36 + t2 = 96/45<BR>\n" );
document.write( "that makes t2 = 96/45 - 48/36 = .8\r<BR>\n" );
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document.write( "you now have:\r<BR>\n" );
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document.write( "r1 = 36<BR>\n" );
document.write( "t1 = 48/36<BR>\n" );
document.write( "r2 = v<BR>\n" );
document.write( "t2 = .8\r<BR>\n" );
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document.write( "you know that r2 * t2 = 48 and you know that r2 = v and t2 = .8, so you get v * .8 = 48.<BR>\n" );
document.write( "solve for v to get v = 48/.8 = 60\r<BR>\n" );
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document.write( "that's your solution.\r<BR>\n" );
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document.write( "you now have:\r<BR>\n" );
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document.write( "r1 = 36<BR>\n" );
document.write( "t1 = 48/36<BR>\n" );
document.write( "r2 = 60<BR>\n" );
document.write( "t2 = .8\r<BR>\n" );
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document.write( "since r1 * t1 + r2 * t2 = r * t, the formula becomes:\r<BR>\n" );
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document.write( "36 * 48/36 + 60 * .8 = 45 * 96/45\r<BR>\n" );
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document.write( "simplify to get 48 + 48 = 96 which is true, confirming the solution is correct.\r<BR>\n" );
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