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What is the distance traveled by the car traveling East in the following problem.Two...

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catd1115 | Middle School Teacher | (Level 3) Assistant Educator

Posted February 20, 2012 at 11:45 PM via web

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What is the distance traveled by the car traveling East in the following problem.

Two cars leave an intersection. Once car travels north; the other travels east. When the car traveling north had gone 30 miles, the distance between the cars was 10 miles more than twice the distance traveled by the car heading east. Find the distance between the cars at that time.

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted February 21, 2012 at 12:37 AM (Answer #1)

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The problem is: Two cars leave an intersection. Once car travels north; the other travels east. When the car traveling north had gone 30 miles, the distance between the cars was 10 miles more than twice the distance traveled by the car heading east. Find the distance between the cars at that time.

When the car traveling north has gone 30 miles, let the distance traveled by the car traveling east be x. It is given that the distance between the cars is 10 miles more than twice the distance traveled by the car heading east.

The distance between the cars is `sqrt(30^2 + x^2)` .

Also `sqrt(30^2 + x^2)` = 10 + 2*x

square both the sides

900 + x^2 = 100 + 4x^2 + 40x

=> 3x^2 + 40x - 800 = 0

x1 = `(-40 + sqrt 11200)/6`

=> `-40/6 + sqrt 11200/6`

The other root is negative and can be ignored.

The distance traveled by the car traveling east is `-40/6 + sqrt 11200/6`

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