Question 1127553
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(Comment before I talk about a solution method....  Crews don't row for 3 hours straight....)<br>
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>
With formal algebra, we can then say x+y=7 and x-y=3 and solve the pair of equations.<br>
Of course that is a valid solution method.<br>
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>
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>
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>
So by simple arithmetic and logical reasoning, the two numbers are 5 and 2.<br>
So the crew's speed is 5mph and the current's speed is 2mph.<br>
Here is another very different problem that is common on tests in math competitions that can be solved by the same logical reasoning.<br>
"The sum of two numbers is 22; their difference is 4.  Find the product of the two numbers."<br>
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>
So the answer to the problem is 13*9 = 117.