
please help
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?
a)–4 ft/sec
b)14 ft/sec
c)50 ft/sec
d)68 ft/sec

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 $\displaystyle a^2+b^2=c^2$ Good. Now differentiate and see what you can plug in. $\displaystyle 2a\frac{da}{dt}+2b\frac{db}{dt}=2c\frac{dc}{dt}$ 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.