Acar travels down a highway at 45 m/s. an observer stands 200 m from the highway.how fast is the distance from the observer to the car increasing when the car passes in front of the observer? how fast is the distance increasing  40  s later?

Check the picture below.

so, the left-side is when the car is right in front of the observer, at that point, notice the y-distance, is pancaked, so is 0, but increasing, we know dy/dt is 45 m/s, and notice the "r" distance, is the same as the "x" distance, keeping in mind that whilst "r" is increasing or moving about, "x" is static, is a constant.



now, 40 seconds later, since the car is going at 45 m/s, in 40 seconds it has covered 40 * 45 meters, or 1800, so y = 1800, x = 200, what is "r"?

Depends if you are nailing all 4 sides together then it would be 15 picture frames because 60 nails divided by 4 nails each picture frame equals 15 picture frames.