Two cars are each 100 miles away from the town of Tucumcari, one directly to the north and the other directly to the east. The car to the north is heading toward the town at 60 miles per hour, while the one to the east is heading toward the town at 30 miles per hour. How fast are the cars approaching each other?

Question

Quizplus · Accepted Answer

The rate at which the distance between the cars decreases is given by the derivative of the distance function. Using the Pythagorean theorem, the distance between the cars is $d = \sqrt{x^2 + y^2}$, where $x$ and $y$ are the distances of the cars from the town. Differentiating and substituting the given speeds, the rate is $45\sqrt{2} \mathrm{mi/h}$.

Two Cars Are Each 100 Miles Away from the Town 2002mi/h200 \sqrt { 2 } \mathrm { mi } / \mathrm { h }2002​mi/h

Two Cars Are Each 100 Miles Away from the Town $200 \sqrt { 2 } \mathrm { mi } / \mathrm { h }$