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
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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?
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
