SOLUTION: If two planes leave the same airport at 1:00 PM, how many miles apart will they be at 3:00 PM if one travels directly north at 150 mph and the other travels directly west at 200 mp

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Plane A travels due north at 150 mph for 2 hours, it will go 300 miles.
Plane B travels due west at 200 mph for 2 hours, it will go 400 miles.
Draw the two vectors and you will see that they make two sides of a right triangle. The distance between the two planes at the end of two hours is just the hypotenuse of this triangle.
You could use the Pythagorean theorem (c^2 = a^2 + b^2) to find the distance...or you could recognise that 300 and 400 are two of a pythagorean triplet (300, 400, 500) and the third number of this triplet is 500.
So, the planes will be 500 miles aprt at the end of two hours.