document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1120780>Question 1120780</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A boat is rowed 10 miles downstream in two hours, then rowed the same distance<BR>\n" );
document.write( "upstream in 10/3 hours. Find the rate of the boat in still water and the rate of the current.<BR>\n" );
document.write( " </SPAN>\n" );
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document.write( "A basic type of problem that is easily solved with basic algebra.<br><BR>\n" );
document.write( "You are looking for two unknown numbers -- the rate of the boat and the speed of the current.  So define variables to represent those two numbers.<br><BR>\n" );
document.write( "let b = boat speed<BR>\n" );
document.write( "let c = current speed<br><BR>\n" );
document.write( "Then observe that the effective speed upstream will be b-c (the current is opposing the boat) and the effective downstream speed will be b+c (the current is aiding the boat).  So<br><BR>\n" );
document.write( "upstream speed = b-c<BR>\n" );
document.write( "downstream speed = b+c<br><BR>\n" );
document.write( "Then distance is rate times time, so write equations that say the upstream and downstream distances are each 10 miles.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2810%2F3%29%28b-c%29+=+10 ALIGN=MIDDLE  ALT=\"%2810%2F3%29%28b-c%29+=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%28b-c%29+=+30 ALIGN=MIDDLE  ALT=\"10%28b-c%29+=+30\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> {{10b-10c = 30}}}<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28b%2Bc%29+=+10 ALIGN=MIDDLE  ALT=\"2%28b%2Bc%29+=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" > -->  2b+2c = 10}}}<br><BR>\n" );
document.write( "Multiply the second equation by 5 and add the two equations to eliminate c:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10b-10c+=+30 ALIGN=MIDDLE  ALT=\"10b-10c+=+30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10b%2B10c+=+50 ALIGN=MIDDLE  ALT=\"10b%2B10c+=+50\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Add these two equations to solve for b; then use that value in either of the original equations to solve for c.<br><BR>\n" );
document.write( "Note that there are many different ways to set up the problem for solving.  Here is a completely different approach that seems to make the work easier.<br><BR>\n" );
document.write( "The 10 miles upstream take 10/3 hours, so the effective upstream rate b-c is 10/(10/3) = 3mph.<BR>\n" );
document.write( "The 10 miles downstream take 2 hours, so the effective downstream rate is b+c = 5mph.<br><BR>\n" );
document.write( "Now the problem can be solved very easily by inspection: b+c=5 and b-c+3; clearly b=4 and c=1. </SPAN>\n" );
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