A car traveling at a rate of 30 ft/sec is approaching an intersection. When the car is 120 ft from the intersection, a truck traveling at a rate of 40 ft/sec crosses the intersection. If the roads are at right angles to each other and the truck leaves the intersection after 2 seconds, how fast are the car and the truck separating when the truck leaves the intersection?
Apr 2nd 2006, 07:29 AM
Ok. Draw a right triangle. Say a is the distance of the car from the intersection. Say b is the distance of the truck from the intersection, and say c is the distance between the car and the truck. You know the equality Good. Now differentiate and see what you can plug in. You know everything here but c, and dc/dt (which you are solving for) You can use right triangles to solve for c at t=2, and then you should have you answer.