SOLUTION: Two cars leave an intersection at the same time, one traveling north and the other traveling east. Sometime later, they are 20 miles apart, and the car going east has traveled 4 mi
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Question 1150371: Two cars leave an intersection at the same time, one traveling north and the other traveling east. Sometime later, they are 20 miles apart, and the car going east has traveled 4 miles farther than the other car. How far has each car traveled? Answer by VFBundy(438) (Show Source):
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x² + (x + 4)² = 20²
x² + (x² + 8x + 16) = 400
2x² + 8x + 16 = 400
2(x² + 4x + 8) = 400
x² + 4x + 8 = 200
x² + 4x - 192 = 0
(x - 12)(x + 16) = 0
x = 12 and x = -16. Since using x = -16 would give both sides negative lengths, we can throw this result out. We are left with x = 12.
When we plug in x = 12, we can see the car travelling north has gone 12 miles, and the car travelling east has gone 16 miles.
