document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1115037>Question 1115037</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Jessie paddled her canoe 20 miles upstream, then paddled back. If the speed of the current was<BR>\n" );
document.write( "3 mph and the total trip took 7 hours, what was Jessie’s speed? </SPAN>\n" );
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document.write( "If x is her speed in still water, then her speed upstream is x-3, and her speed downstream is x+3.<br><BR>\n" );
document.write( "The time for the upstream trip is 20/(x+3); the time for the downstream trip is 20/(x-3).<br><BR>\n" );
document.write( "Since the total time is 7 hours...<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20%2F%28x-3%29%2B20%2F%28x%2B3%29+=+7 ALIGN=MIDDLE  ALT=\"20%2F%28x-3%29%2B20%2F%28x%2B3%29+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Multiply both sides of the equation by the common denominator, (x+3)(x-3); you will get a quadratic equation which has one positive root and one negative.  Obviously the positive root is the answer to the question.<br><BR>\n" );
document.write( "I leave the details of the algebra to you.<br><BR>\n" );
document.write( "Here is a way to solve the problem without the algebra by using logical reasoning.<br><BR>\n" );
document.write( "Note that the total time for the trip upstream and back is 7 hours.  Not 7.2 hours; not 7 hours, 3 minutes, and 43 seconds.  EXACTLY 7 hours.<br><BR>\n" );
document.write( "Because the total trip time is a whole number of hours, the times for each leg of the trip are almost certain to be whole numbers.<br><BR>\n" );
document.write( "Now look at the basic equation for solving the problem.  20 divided by x+3 should be a whole number; and 20 divided by x-3 should be a whole number.<br><BR>\n" );
document.write( "So you need to find two numbers whose difference is 6 (the difference between x+3 and x-3) that are both divisors of 20.<br><BR>\n" );
document.write( "The divisors of 20 are 1, 2, 4, 5, 10, and 20.  The only two that have a difference of 6 are 4 and 10.<br><BR>\n" );
document.write( "So her upstream speed is 4mph and her downstream speed is 10mph; 20/4 + 20/10 = 5+2 = 7 hours.<br><BR>\n" );
document.write( "And since the speed of the current is 3mph, her speed in still water is 7mph. </SPAN>\n" );
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