document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1376>Question 1376</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Antoine rode his bike the 4 miles to the fair at a relaxed pace. He stayed to long and had to double his speed on the way back in order to get home in time for dinner. If his total time traveling was 3 hours, how fast did he travel in each direction?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #452265 by </B><A HREF=/tutors/aboutme.mpl?userid=melzaren><B>melzaren(3)</B></A><img src=\"/images/stars/iconNewId_16x16.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=melzaren><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=452265\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Regrettably, Khwang's answer is wrong:\r<BR>\n" );
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document.write( "\"Hence, his speed going to the fair was 4 miles/hr,and <BR>\n" );
document.write( "his speed backing home was 8 miles/hr.\"\r<BR>\n" );
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document.write( "The question states that Antoine's total travel time was 3 hours.   If he travelled even 1 hour at 4 miles/h or 8 miles/h he would exceed 3 hours of travelling time.\r<BR>\n" );
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document.write( "\"Antoine rode his bike the 4 miles to the fair at a relaxed pace. \"\r<BR>\n" );
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document.write( "trip to the fair:<BR>\n" );
document.write( "4 miles @ a speed of x mph\r<BR>\n" );
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document.write( "\"He stayed to long and had to double his speed on the way back in order to get home in time for dinner.\"\r<BR>\n" );
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document.write( "trip home:<BR>\n" );
document.write( "4 miles @ a speed of 2x mph\r<BR>\n" );
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document.write( "The question states that the entire trip took three hours, so we will build an equation with = 3 hours on the right hand side.\r<BR>\n" );
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document.write( "Now we include the entire trip on the Left hand side of the equation.   Since we're solving for time we flip the miles/h ratio to h/miles, so that the unit \"miles\" cancels and we're left with hours:  We have an algebraic representation of the speed of the trip above.\r<BR>\n" );
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document.write( "4 miles * h/(x miles)       +  4 miles * h/(2x miles)          = 3 hours<BR>\n" );
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document.write( "miles cancels out:\r<BR>\n" );
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document.write( "4h/x + 4h/2x = 3h\r<BR>\n" );
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document.write( "Get the x out of the denominators by multiplying every term by 2x:\r<BR>\n" );
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document.write( "8h + 4h = 6hx\r<BR>\n" );
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document.write( "12h = 6hx<BR>\n" );
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document.write( "divide through by 6h\r<BR>\n" );
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document.write( "2 = x\r<BR>\n" );
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document.write( "Now we know the value of x, plug it in to the speed ratios above and you have your answer.<BR>\n" );
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