Question 1129304
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Once you find that the speed with the wind 1250/2.5 = 500mph and the speed against the wind is 1000/2.5=400mph, here is a simple and fast way to get the speeds of the plane and the wind without formal algebra.<br>
The speed with the wind is the plane's speed plus the speed of the wind; the speed against the wind is the plane's speed minus the speed of the wind.<br>
So the two numbers 500 and 400 are found, respectively, by starting with a first number and adding a second number, and by starting with the same first number and subtracting the second number.<br>
If you visualize those operations on a number line, you can see that the first number has to be halfway between 500 and 400; then the second number has to be the difference between that first number and either 500 or 400.<br>
Without all the words of explanation, the solution goes like this:<br>
(1) the first number is halfway between 500 and 400: it is 450
(2) the second number is the difference between 450 and 500 (or between 450 and 400), which is 50.<br>
This common sense solution can be used to quickly solve many similar problems.  In its undisguised form, it might look like this:<br>
The sum of two numbers is 30, their difference is 6.  What are the two numbers?<br>
Simple!  The first number is halfway between 30 and 6: (30+6)/2 = 18.  The second number is 30-18 = 12 (or 18-6 = 12).