document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1176759>Question 1176759</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need to know the two variables and the 2 equation for this problem.\r<BR>\n" );
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document.write( "Your aunt and uncle have been visiting your home. Five<BR>\n" );
document.write( "minutes after they drive away, you realize that they forgot<BR>\n" );
document.write( "their luggage. You happen to know that they drive at 25<BR>\n" );
document.write( "miles per hour. So you get in your car and drive at 30 miles<BR>\n" );
document.write( "per hour. How far before you meet </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #804206 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=804206\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> rate * time = distance.\r<BR>\n" );
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document.write( "for the aunt and the uncle:<BR>\n" );
document.write( "their rate is 25 miles per hour.<BR>\n" );
document.write( "the formula for them becomes:<BR>\n" );
document.write( "25 * time = distance.\r<BR>\n" );
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document.write( "for you:<BR>\n" );
document.write( "your rate is 30 miles per hour.<BR>\n" );
document.write( "the formula for you becomes:<BR>\n" );
document.write( "30 * time = distance.\r<BR>\n" );
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document.write( "since we already know your rate and their rate, then the only other two variables in the problem that we don't know would be the time and the distance.\r<BR>\n" );
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document.write( "the two equations that need to be solved are:\r<BR>\n" );
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document.write( "25 * time = distance<BR>\n" );
document.write( "30 * time = distance\r<BR>\n" );
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document.write( "since the time that they traveled is 5 minutes less than the time that they traveled because they traveled 5 minutes before you started, then we can change the equations to be:\r<BR>\n" );
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document.write( "25 * time = distance<BR>\n" );
document.write( "30 * (time - 5/60) = distance\r<BR>\n" );
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document.write( "since the speeds are in miles per hour, then the time needs to be in hours.<BR>\n" );
document.write( "5 minutes divided by 60 is equal to 5/60 hours.<BR>\n" );
document.write( "since you had to travel 5 minutes less than them, then you had to travel 5/60 hours less than them.<BR>\n" );
document.write( "5 minutes is equivalent to 5/60 hours. <BR>\n" );
document.write( "we could have simplified at this point, but it 's not necessary to solve the problem.\r<BR>\n" );
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document.write( "since the distance is the same, we can replace the distance with its equivalent in one of the equations to get:\r<BR>\n" );
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document.write( "25 * time = 30 * (time - 5/60)\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "25 * time = 30 * time - 150/60.\r<BR>\n" );
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document.write( "subtract 25 * time from both sides of the equation and add 150/60 to both sides of the equation to get:\r<BR>\n" );
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document.write( "150/60 = 30 * time - 25 * time\r<BR>\n" );
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document.write( "simplify to get:<BR>\n" );
document.write( "150/60 = 5 * time\r<BR>\n" );
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document.write( "solve for time to get:\r<BR>\n" );
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document.write( "time = (150/60)/5 = 150/300 = 1/2 of an hour.\r<BR>\n" );
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document.write( "he caught up to them in 1/2 of an hour.\r<BR>\n" );
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document.write( "go back to the original equations to see if that makes sense and to solve for the distance.\r<BR>\n" );
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document.write( "the two original equations are:\r<BR>\n" );
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document.write( "25 * time = distance<BR>\n" );
document.write( "30 * (time - 5/60) = distance\r<BR>\n" );
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document.write( "when time = 1/2, these equatons become:\r<BR>\n" );
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document.write( "25 * 1/2 = distance = 12.5 miles.<BR>\n" );
document.write( "30 * (1/2 - 5/60) = distance = 30 * (30/60 - 5/60) = 30 * 25/60 = 25/2 = 12.5 miles.\r<BR>\n" );
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document.write( "the distance is the same at 12.5 miles.\r<BR>\n" );
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document.write( "you caught up with them 12.5 miles from the house.<BR>\n" );
document.write( "they were traveling for half an hour which is equal to 30 minutes.<BR>\n" );
document.write( "you were traveling for 25/60 of an hour which is equal to 25 minutes.<BR>\n" );
document.write( "since they left 5 minutes ahead of you, you were traveling 5 minutes less than them when you caught up with them.\r<BR>\n" );
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document.write( "it all checks out.<BR>\n" );
document.write( "the distance was 12.5 miles from the house when you caught up with them.<BR>\n" );
document.write( "that's your answer.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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