I'm doing the final exam and need help setting up problem #6: 6. A highway patrol plane is flying 1 mile above a long, straight road, with constant ground speed of 120 m.p.h. Using radar, the pilot detects a car whose distance from the plane is 1.5 miles and decreasing at a rate of 136 m.p.h. How fast is the car traveling along the highway? (Hint: You may give an exact answer, or use the fact that √ 5 ≈ 2.2.)

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I'm doing the final exam and need help setting up problem #6: 6. A highway patrol plane is flying 1 mile above a long, straight road, with constant ground speed of 120 m.p.h. Using radar, the pilot detects a car whose distance from the plane is 1.5 miles and decreasing at a rate of 136 m.p.h. How fast is the car traveling along the highway? (Hint: You may give an exact answer, or use the fact that √ 5 ≈ 2.2.)

OCW Scholar - Single Variable Calculus
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Here is my work on my paper so far...but just don't know how to proceed.
I worked out the problem and this is the setup I used. Can you please tell me the answer you found so I can also know if I approached this correctly.
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Hey, yes, I eventually think I figured this out. I set up the same as you and then did implicit differentiation. My final answer was 182.5 mph. Did you find a similar result?

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Not exactly, in my case 182.5mph was the combined rate of the plane and the car together. So, the value of x in my diagram decreases at 182.5mph. 120mph of this decrease is contributed by the plane so i got a rate of 62.5mph for the car.
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Yes, very good point! I was wondering if mine was right because it didn't seem to be realistic. Thanks for your input!

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