document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=100914>Question 100914</A>: <I><SPAN STYLE=\"word-break: break-all;\"> John walks the 15 meters from the front door of his house to his moped at<BR>\n" );
document.write( "a constant rate of speed. Having forgotten to lock the front door, he runs the 15 meters<BR>\n" );
document.write( "back to the front door along the same path. His speed running is 2 m/sec faster than<BR>\n" );
document.write( "his speed walking. If the total time to walk to the car and run back to the door was 8<BR>\n" );
document.write( "seconds, what was John’s walking speed?<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 #73450 by </B><A HREF=/tutors/aboutme.mpl?userid=TP><B>TP(29)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=TP><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=73450\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let w be the walking speed, then w+2 must be the running speed (since we're told that his running speed is 2m/s more than his walking speed).\r<BR>\n" );
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document.write( "Let the walking time be t seconds and the running time be T seconds\r<BR>\n" );
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document.write( "Now using these facts: distance= average speed*time,\r<BR>\n" );
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document.write( "                       the distance is 15 metres in each case( walking and running),\r<BR>\n" );
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document.write( "                       the factors of 15 are 5 and 3 and\r<BR>\n" );
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document.write( "                       t+T= 8 (given)\r<BR>\n" );
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document.write( "                       <BR>\n" );
document.write( "we can find w BY INSPECTION as follows:\r<BR>\n" );
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document.write( "Since 15=3*5=w*t<BR>\n" );
document.write( "and<BR>\n" );
document.write( "      15=5*3=(w+2)*T then it follows that w=3,t=5 and T=3.\r<BR>\n" );
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document.write( "So the walking speed,w,is 3m/sec.ANS \r<BR>\n" );
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document.write( "You can of course solve the question using algebra but why do that with such a trivial question.<BR>\n" );
document.write( "In an exam situation time is of the essence and a solution BY INSPECTION is totally valid provided you show what it is based upon.\r<BR>\n" );
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document.write( "Using algebra and the definitions given above a possible solution might be as follows:\r<BR>\n" );
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document.write( "15=w*t so t=15/w<BR>\n" );
document.write( "Similarly,15=(w+2)*T so T=15/(w+2).\r<BR>\n" );
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document.write( "But t+T=8 and so (15/w)+(15/(w+2))=8<BR>\n" );
document.write( "This leads to (1/w)+(1/(w+2))=8/15<BR>\n" );
document.write( "Adding the two algebraic fractions together we get:\r<BR>\n" );
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document.write( "(w+2+w)/w(w+2) = 8/15\r<BR>\n" );
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document.write( "Hence 2w+2 = 8 (i) and w(w+2) = 15 (ii)<BR>\n" );
document.write( "Considering 2w+2 = 8 it follows that w+1 = 4 (dividing both sides by 2)<BR>\n" );
document.write( "And so w = 3<BR>\n" );
document.write( "That is, the walking speed is 3m/sec.ANS </SPAN>\n" );
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