Two cars leave an intersection at the same time. One is headed south at a consta

Question

Two cars leave an intersection at the same time. One is headed south at a constant speed of 30 miles per hour, the other is headed west at a constant speed of 40 miles per hour. Express the distance d between the cars as a function of the time t. [Hint: At t = 0, the cars leave the intersection.] Two cars leave an intersection at the same time. One is headed south at a constant speed of 30 miles per hour, the other is headed west at a constant speed of 40 miles per hour. Express the distance d between the cars as a function of the time t. [Hint: At t = 0, the cars leave the intersection.]

Explanation / Answer

The distance between the two cars will be the length of the hypotenuse as each car travels in its given direction. distance = rate X time so for the car headed south its distance traveled at time t is 30t likewise, the car headed west travels a distance at time t of 40t using the pythagorean theorem we can calculate the distance between the two cars at any time t. distance = sqrt( (30t)^2 + (40t)^2) distance = sqrt( 900t^2 + 1600t^2)

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