SOLUTION: When a crew rows with the current, it travels 21 miles in 3 hours. Against the current, the crew rows 9 miles in 3 hours. Let x= the crew's rowing rate in still water and let

Question 1127553: When a crew rows with the current, it travels
21 miles in
3 hours. Against the current, the crew rows
9 miles in
3 hours. Let
x= the crew's rowing rate in still water and let
y=the rate of the current. Find the rate of rowing in still water and the rate of the current.
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39620) (Show Source): You can put this solution on YOUR website!
-----
When a crew rows with the current, it travels
21 miles in 3 hours.
-
Against the current, the crew rows 9 miles in
3 hours.
-
x= the crew's rowing rate in still water and let
y=the rate of the current. Find the rate of rowing in still water and the rate of the current.
------

Use Elimination Method.
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

(Comment before I talk about a solution method.... Crews don't row for 3 hours straight....)

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.

With formal algebra, we can then say x+y=7 and x-y=3 and solve the pair of equations.

Of course that is a valid solution method.

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.

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.

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.

So by simple arithmetic and logical reasoning, the two numbers are 5 and 2.

So the crew's speed is 5mph and the current's speed is 2mph.

Here is another very different problem that is common on tests in math competitions that can be solved by the same logical reasoning.

"The sum of two numbers is 22; their difference is 4. Find the product of the two numbers."

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.

So the answer to the problem is 13*9 = 117.
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