document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1192951>Question 1192951</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A kayak can travel 48  miles downstream in 4 ​hours, while it would take 24 hours to make the same trip upstream. Find the speed of the kayak in still​ water, as well as the speed of the current. Let k represent the speed of the kayak in still​ water, and let c represent the speed of the current. </SPAN>\n" );
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document.write( "The downstream speed is 48/4 = 12mph; the upstream speed is 48/24 = 2mph.<br><BR>\n" );
document.write( "If you need a solution using formal algebra....<br><BR>\n" );
document.write( "k+c=12  (downstream, the current speed adds to the speed of the kayak)<BR>\n" );
document.write( "k-c=2  (upstream, the current speed subtracts from the speed of the kayak)<br><BR>\n" );
document.write( "Add the two equations; variable c is eliminated;<br><BR>\n" );
document.write( "2k=14<BR>\n" );
document.write( "k=7<br><BR>\n" );
document.write( "Find the speed of the current using k=7 in either of the earlier equations.<br><BR>\n" );
document.write( "7+c=12<BR>\n" );
document.write( "c=5<br><BR>\n" );
document.write( "ANSWER: speed of the kayak = k=7; speed of the current = c=5<br><BR>\n" );
document.write( "There are a huge number of problems where you end up with (or are given at the beginning) the fact that the sum of two numbers is A and their difference is B.  In any case like that, one of the numbers is the average of A and B; and the other is the difference between that average and either of the numbers.<br><BR>\n" );
document.write( "In this example, with the sum of the two speeds being 12 and the difference being 2, one of the numbers is the average of 12 and 2, which is 7; and the other number is the difference between 7 and 12 (or between 7 and 2), which is 5.  So the kayak speed is 7mph and the current speed is 5mph.<br><BR>\n" );
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