SOLUTION: Two cars leave an intersection. one travels north; the other car travels west. when the car traveling north had gone 48 miles, the distance between the cars was 8 miles more than t

Question 744896: Two cars leave an intersection. one travels north; the other car travels west. when the car traveling north had gone 48 miles, the distance between the cars was 8 miles more than three times the distance traveled by the car heading west. find the distance between the cars at that time.

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Two cars leave an intersection. one travels north; the other car travels west.
when the car traveling north had gone 48 miles, the distance between the cars was 8 miles more than three times the distance traveled by the car heading west.
find the distance between the cars at that time.
:
This is a pythag problem, the distance between the cars is the hypotenuse
:
let w = the distance traveled by the westbound car
:
"the distance between the cars was 8 miles more than three times the distance traveled by the car heading west." therefore
3w + 8 = the distance between the cars
:
48^2 + w^2 = (3w+8)^2
FOIL (3w+8)(3w+8)
2304 + w^2 = 9w^2 + 48w + 64
2304 = 9w^2 - w^2 + 24w + 64
Arrange as a quadratic equation
8w^2 + 48w + 64 - 2304 = 0
8w^2 + 48w - 2240 = 0
Simplify, divide by 8:
w^2 + 6w - 280 = 0
Factors to
(w+20)(w-14) = 0
the positive solution is all we want here
w = 14 mi traveled by the west bound car
then
3(14) + 8 = 50 mi between the cars
:
:
See if that checks out on a calc
enter results is 50, confirms our solution
"

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