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
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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.
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.
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This is a pythag problem, the distance between the cars is the hypotenuse
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let w = the distance traveled by the westbound car
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"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
:
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See if that checks out on a calc
enter results is 50, confirms our solution
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