document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1127553>Question 1127553</A>: <I><SPAN STYLE=\"word-break: break-all;\"> When a crew rows with the current, it travels<BR>\n" );
document.write( "21 miles in<BR>\n" );
document.write( "3 hours. Against the current, the crew rows <BR>\n" );
document.write( "9 miles in<BR>\n" );
document.write( "3 hours. Let<BR>\n" );
document.write( "x= the crew's rowing rate in still water and let <BR>\n" );
document.write( "y=the rate of the current. Find the rate of rowing in still water and the rate of the current. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #743970 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13203)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=743970\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "(Comment before I talk about a solution method....  Crews don't row for 3 hours straight....)<br><BR>\n" );
document.write( "From the given information, we know the downstream speed is 7 mph and the upstream speed is 3 mph.  So we then say the sum of the crew's speed and the current is 7 and the difference between the two speeds is 3.<br><BR>\n" );
document.write( "With formal algebra, we can then say x+y=7 and x-y=3 and solve the pair of equations.<br><BR>\n" );
document.write( "Of course that is a valid solution method.<br><BR>\n" );
document.write( "However, this kind of problem comes in many forms, where the sum of two numbers is one number and the difference is another number.  And there is a simple and fast way to solve a problem like that.<br><BR>\n" );
document.write( "What we know in this problem is that when you start at some number and add a second number, the sum is 7; when you start at the same first number and subtract the same second number, the result is 3.<br><BR>\n" );
document.write( "But simple logical reasoning tells you that the first number is halfway between 7 and 3, which is 5; the second number is how far 3 and 7 are away from 5, which is 2.<br><BR>\n" );
document.write( "So by simple arithmetic and logical reasoning, the two numbers are 5 and 2.<br><BR>\n" );
document.write( "So the crew's speed is 5mph and the current's speed is 2mph.<br><BR>\n" );
document.write( "Here is another very different problem that is common on tests in math competitions that can be solved by the same logical reasoning.<br><BR>\n" );
document.write( "\"The sum of two numbers is 22; their difference is 4.  Find the product of the two numbers.\"<br><BR>\n" );
document.write( "Solution:  The first number is halfway between 22 and 4, which is 13.  The second number is how far away 22 and 4 are from 13, which is 9.<br><BR>\n" );
document.write( "So the answer to the problem is 13*9 = 117. </SPAN>\n" );
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