document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=68171>Question 68171</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0471659584/algebrahomeworkh>College Algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> A speedboat takes 1 hour longer to go 24 miles up a river than to return.  If the boat cruises at 10 miles per hour in still water, what is the rate of the current?\r<BR>\n" );
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document.write( "If R*T=D, and R is speed + or - current, how can you find the rate without the time, and how can you find the time without the rate? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #48475 by </B><A HREF=/tutors/aboutme.mpl?userid=ptaylor><B>ptaylor(2198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ptaylor><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=ptaylor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=48475\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "If R*T=D, and R is speed + or - current, how can you find the rate without the time, and how can you find the time without the rate?\r<BR>\n" );
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document.write( "THE KEY WAS WHEN WE WERE TOLD THAT IT TAKES ONE HOUR LONGER TO GO UPSTREAM THAN DOWNSTREAM BECAUSE T=D/R AND WE ARE TOLD THAT:\r<BR>\n" );
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document.write( "D/R(Upstream) minus 1 equals D/R (DOWNSTREAM)\r<BR>\n" );
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document.write( "Let x=rate of current\r<BR>\n" );
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document.write( "distance(d)=rate(r) times time(t) or d=rt  or t=d/r\r<BR>\n" );
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document.write( "distance upstream=distance downstream=24 mi\r<BR>\n" );
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document.write( "rate upstream=10-x\r<BR>\n" );
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document.write( "rate downstream=10+x\r<BR>\n" );
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document.write( "time upstream=(distance upstream)/(rate upstream)=24/(10-x)<BR>\n" );
document.write( "time downstream=(distance downstream)/(rate downstream)=24/(10+x)\r<BR>\n" );
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document.write( "Now, we are told that time upstream minus one hour equals time downstream.  So our equation to solve is:\r<BR>\n" );
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document.write( "24/(10-x)-1=24/(10+x)  Multiply both sides by (10-x)(10+x)\r<BR>\n" );
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document.write( "24(10+x)(10-x)/(10-x)-1(10-x)(10+x)=24(10-x)/(10+x)/(10+x)  clear fractions\r<BR>\n" );
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document.write( "24(10+x)-(10-x)(10+x)=24(10-x)  clear parens\r<BR>\n" );
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document.write( "240+24x-100-10x+10x+x^2=240-24x  subtract 240 from and add 24x to both sides\r<BR>\n" );
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document.write( "240-240+24x+24x-100+x^2=240-240-24x+24x  collect like terms\r<BR>\n" );
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document.write( "x^2+48x-100=0 ----------------quadratic equation in standard form\r<BR>\n" );
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document.write( "This equation can be factored:\r<BR>\n" );
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document.write( "(x+50)(x-2)=0\r<BR>\n" );
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document.write( "x=-50 mph----------------discount the negative value for speed\r<BR>\n" );
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document.write( "and \r<BR>\n" );
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document.write( "x=2 mph----------------------speed of the current\r<BR>\n" );
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document.write( "CK<BR>\n" );
document.write( "10-x=10-2= 8 mph -----------------------speed upstream<BR>\n" );
document.write( "10+x=10+2=12 mph--------------------------speed downstream\r<BR>\n" );
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document.write( "time upstream=24/8=3 hours<BR>\n" );
document.write( "time downstream=24/12=2 hours\r<BR>\n" );
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document.write( "so 3-2=1----takes 1 hour longer upstream\r<BR>\n" );
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document.write( "Hope this helps -----ptaylor<BR>\n" );
document.write( " </SPAN>\n" );
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