document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1166743>Question 1166743</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A lady traveled 100 kilometers at a rate of 30 kilometers an hour. If she wants her return trip to be three-fourths of her trip, at what rate must she return? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #791259 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=791259\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> r*t=d<BR>\n" );
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( "the lady traveled 100 kilometers at a rate of 30 kilometers per hour.<BR>\n" );
document.write( "the formula for her becomes 30 * t = 100<BR>\n" );
document.write( "solve for t to get t = 100 / 30 = 10/3 hours.\r<BR>\n" );
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document.write( "she wants her return trip to take 3/4 of the time it took her to get to her destination.\r<BR>\n" );
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document.write( "3/4 * t = 3/4 * 10/3 = 30/12 = 10/4.\r<BR>\n" );
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document.write( "instead of taking 10/3 hours, the trip back should take 10/4 hours.\r<BR>\n" );
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document.write( "the formula of r * t = d becomes:<BR>\n" );
document.write( "r * 10/4 = 100<BR>\n" );
document.write( "solve for r to get:<BR>\n" );
document.write( "r = 400/10 = 40\r<BR>\n" );
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document.write( "going there she travels at 30 kilometers per hour.<BR>\n" );
document.write( "coming back she travels at 40 kilometers per hour.\r<BR>\n" );
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document.write( "the formula for going there is 30 * t = 100<BR>\n" );
document.write( "the formula for coming back is 40 * t = 100\r<BR>\n" );
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document.write( "the time for going there is 100 / 30 hours.<BR>\n" );
document.write( "the time for coming back is 100 / 40 hours.\r<BR>\n" );
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document.write( "3/4 * 100 / 30 is equal to 300 / 120 which is equal to 100 / 40.<BR>\n" );
document.write( "that's the time it takes to get back, confirming the solution is correct.\r<BR>\n" );
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document.write( "the solution is that she must comes back at the rate of 40 kilometers per hour.\r<BR>\n" );
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document.write( "i worked in fractions because the decimals were repeating.<BR>\n" );
document.write( "you can work in decimals as well as long as you round to enough decimal digits so that the repeating decimals will still give you the correct answer.\r<BR>\n" );
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document.write( "for example, i did the following:\r<BR>\n" );
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document.write( "r * t = d becomes 30 * t = 100 when she is going to her destination.<BR>\n" );
document.write( "solve for t to get t = 100/30 = 3.33333 rounded to 5 decimal places.<BR>\n" );
document.write( "she wants t on the return trip to be equal to 3/4 of the time going.<BR>\n" );
document.write( "3/4 * t = 3/4 * 3.33333 = 2.5<BR>\n" );
document.write( "the formula of r * t on the return trip becomes r * 2.5 = 100<BR>\n" );
document.write( "solve for r to get r = 100 / 2.5 = 40 hours.\r<BR>\n" );
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document.write( "working in decimal wasn't as bad as i thought.<BR>\n" );
document.write( "either way, you get the same answer.<BR>\n" );
document.write( "the answer is 40 kilometers per hour.\r<BR>\n" );
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document.write( "your solution is that she would have to travel back at 40 kilometers per hour so that the time required on the return trip is 3/4 of the time taken getting to her destination.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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