Question 1137365
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The given distance and the given times tell you the upstream speed is 2mph and the downstream speed is 6mph.  Algebraically, with k for the speed of the kayak in still water and c for the speed of the current, that can be represented by<br>
k+c = 6
k-c = 2<br>
Then you can solve the problem using formal algebra using those two equations.<br>
But this is an example of a wide variety of problems in which you get to a point where the information lets you find the sum and difference of two numbers.  In that kind of problem, you can finish the problem easily by some simple logical reasoning.<br>
Think of the sum and difference of the two numbers on a number line.  You start at one of the numbers; if you add the second number, you end up one place, and if you subtract the second number, you end up at a second place.  Since you went the same distance in each direction to get to those two ending places, the place you started has to be halfway between those two ending places.<br>
So given that the sum of two numbers is A and the difference is B, the first number is halfway between A and B.<br>
In this problem, the sum of the kayak's speed and the river's speed is 6mph; the difference is 2mph.  That means the kayak's speed is halfway between 6mph and 2pmh, which is 4mph, and that makes the speed of the current 2mph.<br>
So to solve this problem, once you have the upstream and downstream speeds of 2mph and 6mph, you can immediately conclude that the kayak's speed is 4mph and the speed of the current is 2mph.<br>
Here is another common type of problem that uses the same simple solution method.<br>
The sum of two numbers is 25; their difference is 11.  Find the two numbers.<br>
You can quickly reason that one number is halfway between 25 and 11, which is 18; then the other number must be 7.