document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=137672>Question 137672</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/9780321319081/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> the tugboat moves at a rate of 10mph in still water. it travels 24 mi upstream and 24 mi downstream in a total time of 5 hr. what is the speed of the current?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #100696 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=100696\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Distance(d) equals Rate(r) times Time(t) or d=rt;  r=d/t and t=d/r\r<BR>\n" );
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document.write( "Let r=speed of the current<BR>\n" );
document.write( "tugboat's speed upstream=10-r<BR>\n" );
document.write( "tugboat's speed downstream=10+r\r<BR>\n" );
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document.write( "Time for tugboat to travel upstream=24/(10-r)<BR>\n" );
document.write( "Time for tugboat to travel downstream=24/(10+r)\r<BR>\n" );
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document.write( "Now we are told that the sum of the above two times equals 5 hours, so our equation to solve is:\r<BR>\n" );
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document.write( "24/(10-r)+24/(10+r)=5  multiply each term by (10-r)(10+r)\r<BR>\n" );
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document.write( "24(10+r)+24(10-r)=5(10-r)(10+r)  get rid of parens\r<BR>\n" );
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document.write( "240+24r+240-24r=500-5r^2  subtract 500 from and add 5r^2 to both sides\r<BR>\n" );
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document.write( "240+24r+240-24r-500+5r^2=500-500-5r^2+5r^2  collect like terms\r<BR>\n" );
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document.write( "-20+5r^2=0 rearranging:<BR>\n" );
document.write( "5r^2-20=0  divide each side by 5<BR>\n" );
document.write( "r^2-4=0-------------------------------quadratic in standard form and it can be factored\r<BR>\n" );
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document.write( "(r-2)(r+2)=0<BR>\n" );
document.write( "r=2 mph--------------------speed of the current<BR>\n" );
document.write( "and<BR>\n" );
document.write( "r=-2 mph----------------------DISREGARD--- CURRENT SPEED IS POSITIVE\r<BR>\n" );
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document.write( "ck<BR>\n" );
document.write( "24/(10-2)+24/(10+2)=5<BR>\n" );
document.write( "3+2=5<BR>\n" );
document.write( "5=5\r<BR>\n" );
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document.write( "Hope this helps----ptaylor </SPAN>\n" );
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