Problema 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 that time the two cars are 15 mi. apart. How far did each car travel?
Answer provided by our tutors
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