SOLUTION: two automobiles leave an intersection at the same time. one of them travels west and the other travels south. when the vehicle going south has traveled 24 miles, the distance betwe

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Question 877551: two automobiles leave an intersection at the same time. one of them travels west and the other travels south. when the vehicle going south has traveled 24 miles, the distance between the cars was four miles more than three times the distance traveled by the vehicle traveling west. find the distance between the two automobiles at that time.

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
D%5Bs%5D=24
D=4%2B3D%5Bw%5D
The distance between them is the hypotenuse of a right triangle where the sides are the distance traveled south and the distance traveled west.
Use the Pythagorean theorem,
D%5E2=D%5Bs%5D%5E2%2BD%5Bw%5D%5E2
%284%2BD%5Bw%5D%29%5E2=24%5E2%2BD%5Bw%5D%5E2
16%2B8D%5Bw%5D%2BD%5Bw%5D%5E2=576%2BD%5Bw%5D%5E2
8D%5Bw%5D=560
D%5Bw%5D=70
D=4%2B3%2870%29
highlight%28D=214%29