document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=266535>Question 266535</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Mary runs twice as fast as bob and billy runs at 80% of bob’s pace. What fraction of a mile will billy complete in the same time that mary runs  1/3 of a mile ? express your answer as a common fraction  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #195868 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=195868\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> mary runs twice as fast as bob.\r<BR>\n" );
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document.write( "billy runs 80% as fast as bob.\r<BR>\n" );
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document.write( "this means that bob runs 1/.8 times as fast as billy equals 1.25 times as fast as billy.\r<BR>\n" );
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document.write( "if bob runs at 5 miles per hour, then billy runs at 80% * 5 miles per hour = 4 miles per hour.\r<BR>\n" );
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document.write( "5 miles per hour equals 1.25 times 4 miles per hour.\r<BR>\n" );
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document.write( "now mary runs twice as fast as bob and bob runs 1.25 times as fast as billy.\r<BR>\n" );
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document.write( "this means that mary runs 2 * 1.25 = 2.5 times as fast as billy.\r<BR>\n" );
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document.write( "so if billy runs at 4 miles per hour, then:\r<BR>\n" );
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document.write( "bob runs at 1.25 * 4 = 5 miles per hour, and:\r<BR>\n" );
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document.write( "mary runs at 1.25 * 2 * 4 miles per hour equals 10 miles per hour.\r<BR>\n" );
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document.write( "10 miles per hour is equals to 2 * 5 miles per hour so the ratios are good.\r<BR>\n" );
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document.write( "now if mary runs 1/3 of a mile in T minutes, then:\r<BR>\n" );
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document.write( "mary's rate * T minutes = 1/3 mile.\r<BR>\n" );
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document.write( "but mary's rate is 2.5 times billy's rate, so the formula becomes:\r<BR>\n" );
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document.write( "2.5 * billy's rate * T minutes = 1/3 of a mile.\r<BR>\n" );
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document.write( "if we divide both sides of this equation by 2.5, we get:\r<BR>\n" );
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document.write( "billy's rate * T minutes = 1/3 mile / 2.5 = 1/7.5 * 2/2 = 2/15 of a mile.\r<BR>\n" );
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document.write( "in the same time that mary runs 1/3 of a mile, billy runs 2/15 of a mile.\r<BR>\n" );
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document.write( "1/3 * 5/5 = 5/15.\r<BR>\n" );
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document.write( "5/15 = 2.5 * 2/15\r<BR>\n" );
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document.write( "your answer is billy runs 2/15 of a mile in the same time that mary runs 1/3 of a mile.\r<BR>\n" );
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document.write( "now billy runs .8 times as fast as bob, so we have:\r<BR>\n" );
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document.write( "billy's rate * T minutes = 2/15 of a mile.\r<BR>\n" );
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document.write( "this becomes:\r<BR>\n" );
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document.write( ".8 * bob's rate * T minutes = 2/15 of a mile.\r<BR>\n" );
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document.write( "divide both sides of this equation by .8 to get:\r<BR>\n" );
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document.write( "bob's rate * T minutes = 2/15 of a mile / .8\r<BR>\n" );
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document.write( "this means that:\r<BR>\n" );
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document.write( "bob's rate * T minutes = 2/12 of a mile.\r<BR>\n" );
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document.write( "2/12 of a mile is the same as 1/6 of a mile in T minutes.\r<BR>\n" );
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document.write( "1/6 is half of 1/3 confirming that mary runs twice as fast as bob and covers twice the ground as bob.\r<BR>\n" );
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document.write( "all measurements check out.\r<BR>\n" );
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document.write( "the ratios are good.\r<BR>\n" );
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document.write( "the answer should be also be good.\r<BR>\n" );
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document.write( "billy runs 2/15 of a mile in the same time that mary runs 1/3 of a mile.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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