SOLUTION: two cars leave an intersection, one traveling west and the other south. After some time the faster car is 3 mi farther away from the intersection than the slower car. At the time t

Question 665081: two cars leave an intersection, one traveling west and the other south. After some time the faster car is 3 mi farther away from the intersection than the slower car. At the time the two cars where 15 miles apart.
How far did each car travel?

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
two cars leave an intersection, one traveling west and the other south.
After some time the faster car is 3 mi farther away from the intersection than the slower car.
At the time the two cars where 15 miles apart. How far did each car travel?
:
Let d = distance traveled by the 1st car when they were 15 mi apart
then
(d+3) = distance traveled by the faster car
:
This is pythag problem: a^2 + b^2 = c^2, where
a = d
b = (d+3)
c = 15
:
d^2 + (d+3)^2 = 15^2
FOIL(d+3)(d+3)
d^2 + d^2 + 3d + 3d + 9 = 225
:
2d^2 + 6d + 9 - 225 = 0
2d^2 + 6d - 216 = 0
simplify, divide by 2
d^2 + 3d - 108 = 0
this will factor to
(d+12)(d-9) = 0
the positive solution is all we want here
d = 9 mi, and 12 mi when they were 15 mi apart
:
:
Check this on a calc; enter results: 15
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