document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=184033>Question 184033</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose you are at a river resort and rent a motorboat for 5 hours starting at 7am. You are told that the boat will travel at 8 miles per hour upstream and 12 miles per hour returning. you decide that you would like to go as far up the river as you can and still be back at noon. at what time should you turn back, and how far from the resort will you be at that time? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #138089 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=138089\">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<BR>\n" );
document.write( "Let t=amount of time used to travel upstream<BR>\n" );
document.write( "And (5-t)= amount of time used to travel downstream\r<BR>\n" );
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document.write( "Distance travelled upstream=8*t<BR>\n" );
document.write( "Distance travelled downstream=12(5-t)<BR>\n" );
document.write( "And we know that the above two distances have to be equal, so:<BR>\n" );
document.write( "8t=12(5-t) get rid of parens<BR>\n" );
document.write( "8t=60-12t  add 12t to each side<BR>\n" );
document.write( "8t+12t=60-12t+12t  collect like terms<BR>\n" );
document.write( "20t=60<BR>\n" );
document.write( "t=3 hr-----------------time travelled upstream<BR>\n" );
document.write( "So, 7am + 3 hr=10am--------------time to turn back<BR>\n" );
document.write( "5-t=5-3=2 hr ------------time travelled downstream<BR>\n" );
document.write( "distance upstream =8*t=8*3=24 mi from resort\r<BR>\n" );
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document.write( "ANOTHER WAY:<BR>\n" );
document.write( "let t=time used to travel upstream<BR>\n" );
document.write( "Then 5-t=time used to travel downstream<BR>\n" );
document.write( "Let d=distance travelled upstream; also distance travelled downstream as well as distance from resort when turning back<BR>\n" );
document.write( "7am + t=time to turn back<BR>\n" );
document.write( "t=d/8-----------------------------eq1<BR>\n" );
document.write( "5-t=d/12---------------------------eq2<BR>\n" );
document.write( "substitute t=d/8 from eq1 into eq2<BR>\n" );
document.write( "5-d/8=d/12  multiply each term by 24<BR>\n" );
document.write( "120-3d=2d  add 3d to each side<BR>\n" );
document.write( "5d=120<BR>\n" );
document.write( "d=24 mi----------------------distance from resort when turning back<BR>\n" );
document.write( "substitute d=24 into eq1<BR>\n" );
document.write( "t=24/8=3 hrs----------------time used to travel upstream<BR>\n" );
document.write( "7am+3=10am-------------time to turn back\r<BR>\n" );
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document.write( "Hope this helps---ptaylor </SPAN>\n" );
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