Question 598103
Two airplanes leave simultaneously from an airport. One flies due south; the other flies due east at a rate 20 mph faster than the first airplane. After 1.5 hours, radar indicates that the airplanes are 450 miles apart. What is the ground speed of each airplane? 
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Let x = ground speed of slower plane
then
x+20 = ground speed of faster plane
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Because of the directions the two planes are flying, they form "right angle" (90 degrees).  Therefore, you can use Pythagorean Theorem to solve:
applying the distance formula: d=rt
(1.5x)^2 + (1.5(x+20))^2 = 450^2
2.25x^2 + (1.5x+30)^2 = 202500
2.25x^2 + (1.5x+30)(1.5x+30) = 202500
2.25x^2 + 2.25x+90x+900 = 202500
4.5x^2+90x-201600 = 0
.5x^2+10x-22400 = 0
apply the quadratic formula to solve, which gives us:
x = {201.8962, -221.8962}
throw out the negative solution (extraneous) leaving
x = 202 mph (slower plane)
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faster plane:
x+20 = 202+20 = 222 mph
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details of quadratic follows:
*[invoke quadratic "x", .5, 10, -22400 ]