document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=156080>Question 156080</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am having difficulty setting up the equation for this problem. Thank you for any help.\r<BR>\n" );
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document.write( "An army messenger will travel at a speed of 60 miles per hour on land and in a motorboat whose speed is 20 miles per hour in still water. In delivering a message he will go by land to a dock on a river and then on the river against a current of 4 miles per hour. If he reaches his destination in 4 1/2 hours and then returns to his starting point in 3 1/2 hours, how far did he travel by land and how far by water. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #114939 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=114939\">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( "GOING TO DESTINATION:<BR>\n" );
document.write( "Let d1=distance travelled on land (one way)<BR>\n" );
document.write( "And let d2=distance travelled by boat (one way)<BR>\n" );
document.write( "Then total distance travelled=2d1+2d2<BR>\n" );
document.write( "Time travelled on land=d1/60<BR>\n" );
document.write( "Time travelled by boat=d2/(20-4)=d2/16  (must subtract speed of current)<BR>\n" );
document.write( "Now we are told that the above two times equals 4.5 hr, so:\r<BR>\n" );
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document.write( "d1/60 + d2/16=4.5-------------------------eq1\r<BR>\n" );
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document.write( "RETURNING TO STARTING POINT:<BR>\n" );
document.write( "Time travelled by boat=d2/(20+4)=d2/24-------------(must add speed of current)<BR>\n" );
document.write( "Time travelled on land=d1/60<BR>\n" );
document.write( "And we are told that the above two times equals 3.5 hrs, so:\r<BR>\n" );
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document.write( "d1/60 +d2/24=3.5-------------------------------eq2\r<BR>\n" );
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document.write( "subtract eq2 from eq1:<BR>\n" );
document.write( "d2/16 -d2/24=1 or<BR>\n" );
document.write( "3d2/48-2d2/48=1 and<BR>\n" );
document.write( "d2/48=1  multiply each side by 48<BR>\n" );
document.write( "d2=48 mi;  substitute into eq1<BR>\n" );
document.write( "d1/60+48/16=4.5<BR>\n" );
document.write( "d1/60+3=4.5  subtract 3 from each side<BR>\n" );
document.write( "d1/60=1.5  multiply each side by 60<BR>\n" );
document.write( "d1=90 mi<BR>\n" );
document.write( "Total distance travelled=2d1+2d2=2*90+2*48=180+96=276 mi<BR>\n" );
document.write( "Distance travelled by land=2d1=2*90=180 mi<BR>\n" );
document.write( "Distance travelled by water=2d2=2*48=96 mi\r<BR>\n" );
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document.write( "CK<BR>\n" );
document.write( "90/60+48/16=4.5<BR>\n" );
document.write( "1.5+3=4.5<BR>\n" );
document.write( "4.5=4.5<BR>\n" );
document.write( "and<BR>\n" );
document.write( "48/24+90/60=3.5<BR>\n" );
document.write( "2+1.5=3.5<BR>\n" );
document.write( "3.5=3.5\r<BR>\n" );
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document.write( "Hope this helps---ptaylor<BR>\n" );
document.write( " </SPAN>\n" );
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