# Related Rates - Differentiation

An airplane is flying at an altitude of 8 miles and passes over a radar station. When the airplane is 12 miles from the base of the station, the radar detects that its horizontal distance is changing at a rate of 320 mph. Find how fast the airplane is flying at this point in time.

The question asks to find the speed of the airplane. I know $\displaystyle speed = \frac{distance}{time}$. And, in this case, if I were to draw a right triangle with the radar station and airplane, I get the distance as $\sqrt{80}$ miles. How do I then find time? Do I even have to find time?

If it helps, the answer is 160 mph

• Please show your work. – user114628 Feb 16 '14 at 9:04
• Edited my question. I don't know how to use mathematical notation on the computer though – TheEconomist Feb 16 '14 at 9:08
• @TheEconomist take a look at meta.math.stackexchange.com/q/5020/72616 – Justin Feb 16 '14 at 9:16
• This is a really weird question. The airplane is not traveling up nor down. We are told that the airplane is traveling at a horizontal speed of 320 mph. So isn't the speed that the plane is traveling at 320 mph? – Justin Feb 16 '14 at 9:22
• I think that the altitude and distance from station information yield no useful information. Focusing on the horizontal speed, the relative speed the radar detects will be $2h$ mph (as the radar pulse covers twice the distance), where $h$ is the horizontal speed of the aircraft. So $2h=320$, leading to $h=160$ mph. – Alijah Ahmed Feb 16 '14 at 10:19

This question is dumb