A car leaves an intersection traveling west. Its position 4 sec later is 26 ft from the intersection. At the same time, another car leaves the same intersection heading north so that its position 4 sec later is 26 ft from the intersection. If the speeds of the cars at that instant of time are 12 ft/sec and 10 ft/sec, respectively, find the rate at which the distance between the two cars is changing. Round to the nearest tenth if necessary.
A)15.6 ft/sec
B)3.7 ft/sec
C)3.1 ft/sec
D)36.8 ft/sec

Question

Quizplus · Accepted Answer

Using the Pythagorean theorem, the distance between the cars is the hypotenuse of a right triangle with legs of 26 ft each. The rate of change of this distance can be found using related rates, resulting in approximately 15.6 ft/sec.

A Car Leaves an Intersection Traveling West