document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1039834>Question 1039834</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can someone please help me with this word problem\r<BR>\n" );
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document.write( "From a point on a straight&#8203; road, Chris and Elena ride bicycles in the same direction. Chris rides at 10 mph and Elena rides at 14 mph. In how many hours will they be 30 mi&#8203; apart?<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 #654575 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=654575\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> chris rides at 10 miles an hour.<BR>\n" );
document.write( "elena rides at 14 miles per hour.<BR>\n" );
document.write( "in how many miles will they be 30 miles apart.\r<BR>\n" );
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document.write( "rate * time = distance.\r<BR>\n" );
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document.write( "rate is in miles per hour.<BR>\n" );
document.write( "time is in hours.<BR>\n" );
document.write( "distance is in miles.\r<BR>\n" );
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document.write( "for chris, the formula becomes 10 * time = distance.<BR>\n" );
document.write( "fo4r elena, the formula becomes 14 * time = distance.\r<BR>\n" );
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document.write( "you want to know when the distance between them will be 30 miles.\r<BR>\n" );
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document.write( "since they will have been riding the same time when they are 30 miles apart, we'll let T = the time they both took.\r<BR>\n" );
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document.write( "we'll let D1 = distance that chris rides and D2 = distance that elena rides.\r<BR>\n" );
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document.write( "formula for chris becomes 10 * T = D1<BR>\n" );
document.write( "formula for elena becomes 14 * T = D2\r<BR>\n" );
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document.write( "we know that we want the distance between them to be 30 miles, and we know that elena will have been riding the most miles, so we get D2 - D1 = 30\r<BR>\n" );
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document.write( "Since D2 = 14 * T and D1 = 10 * T, then D2 - D1 = 50 becomes 14 * T - 10 * T = 30.\r<BR>\n" );
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document.write( "factor out the T to get (14 - 10) * T = 30.\r<BR>\n" );
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document.write( "simplify to get 4 * T = 30\r<BR>\n" );
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document.write( "divide both sides of the equation by 4 to get T = 30 / 4 = 7.5 hours.\r<BR>\n" );
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document.write( "to see if we did this correctly, we replace T with 7.5 in the original equations to get:\r<BR>\n" );
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document.write( "rate * time = distance.\r<BR>\n" );
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document.write( "for chris, formula becomes 10 * 7.5 = 75 miles.<BR>\n" );
document.write( "for elena, formula becomes 14 * 7.5 = 105 miles.\r<BR>\n" );
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document.write( "the difference between the miles that elena rides and the miles that chris rides is 30 miles.\r<BR>\n" );
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document.write( "this confirms the solution is correct.\r<BR>\n" );
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document.write( "the solution is they will be 30 miles apart in 7.5 hours.\r<BR>\n" );
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