document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1182755>Question 1182755</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Dan and Jane each have a measuring tape of length 1m. Dan's tape got stuck in a door and was extended by 4cm. Jane left her tape in a pocket and it shrank by 5 cm after washing. However, the centimetre marks on both tapes remained evenly distributed. <BR>\n" );
document.write( "Measuring the schoolyard, Dan noted the length as 23.75m. What length will Jane get measuring the same schoolyard with her tape? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #812833 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=812833\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the length of the tape is 1 meter = 100 centimeters.<BR>\n" );
document.write( "dan's tape measures 1 meter + 4 centimeters = 1.04 meters = 104 centimeters.<BR>\n" );
document.write( "jane's tape measures 1 meter - 5 centimeters = .95 meters = 95 centimeters.\r<BR>\n" );
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document.write( "they both measured the length of the schoolyard with their tape measures.\r<BR>\n" );
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document.write( "the assumption that i think needs to be made is that they both still think their tape measures 1 meter = 100 centimeters.<BR>\n" );
document.write( "in other words, they don't know that the length of their tapes has been distorted.\r<BR>\n" );
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document.write( "dan measures the length of the schoolyard as 23.75 meters = 2375 centimeters.<BR>\n" );
document.write( "this means that he thinks that the length of his tape divides into 2375 by 2375 / 100  = 23.75 times.<BR>\n" );
document.write( "since the length of this tape is actually 104 centimeters, then the length of the schoolyard is actually 23.75 * 104 = 2470 centimeters.\r<BR>\n" );
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document.write( "jane measures the length of the same schoolyard.<BR>\n" );
document.write( "the actual length is 2470 centimeters.<BR>\n" );
document.write( "her tape divides into 2470 centimeters 2470 / 95 = 26 times.<BR>\n" );
document.write( "she thinks that her tape measures 100 centimeters, therefore she records the length of the schoolyard as 26 * 100 = 2600 meters. \r<BR>\n" );
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document.write( "given that the length of the schoolyard is actually 2470 centimeters, ...\r<BR>\n" );
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document.write( "he will measure 2470 / 104 * 100 = 2375 centimeters.<BR>\n" );
document.write( "she will measure 2470 / 95 * 100 = 2600 centimeters.\r<BR>\n" );
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document.write( "i tried to confirm this is true by doing the following.\r<BR>\n" );
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document.write( "assume the actual length of the schoolyard is 1000 centimeters.\r<BR>\n" );
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document.write( "dan's tape will divide into this 1000 / 104 = 9.615384615 times.<BR>\n" );
document.write( "since he thinks his tape measures 100 centimeters, he will report the length as 9.615384615 * 100 = 961.5384615 centimeters.<BR>\n" );
document.write( "his measurement will be 961.5384615 / 1000 = .9615384615 times the actual measurement.\r<BR>\n" );
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document.write( "jane's tape will divide into this 1000 / 95 = 10.52631579 times.<BR>\n" );
document.write( "since she thinks her tape measures 100 centimeters, she will report the length as 1052.631579 centimeters.<BR>\n" );
document.write( "her measurement will be 1052.631579 / 1000 = 1.052631579 times the actual measurement.\r<BR>\n" );
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document.write( "take these ratios and apply to the problem at hand and you will get.\r<BR>\n" );
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document.write( "2375 / .9615384615 = 2470<BR>\n" );
document.write( "2600 / 1.052631579 = 2470.\r<BR>\n" );
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document.write( "it appears that i did this right.<BR>\n" );
document.write( "if so, then:\r<BR>\n" );
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document.write( "dan measures the schoolyard as 2375 centimeters = 23.75 meters.<BR>\n" );
document.write( "jane measures the schoolyard as 2600 centimeters 26 meters.<BR>\n" );
document.write( "the actual measurement of the schoolyard is 2470 centimeters = 24.70 meters.\r<BR>\n" );
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document.write( "your solution should be that jane measures the schoolyard as 26 meters.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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