Expert: Paul Klarreich - 1/6/2008

Question
Hello professor, please help me with the following problem:
A man 5 ft tall walks at the rate of 5 ft/sec toward a street light that is 15 ft above the ground. At what rate is the length of his shadow changing when he is 10 ft from the base of the light?

I could easily solve this problem if the question would not include the 10 ft. thank you for your time.

Answer
Questioner:   sinclair
Category:  Calculus
Private:  No
 
Subject:  related rates
Question:  Hello professor, please help me with the following problem:
A man 5 ft tall walks at the rate of 5 ft/sec toward a street light that is 15 ft above the ground. At what rate is the length of his shadow changing when he is 10 ft from the base of the light?

I could easily solve this problem if the question would not include the 10 ft. thank you for your time.
.............................................................
Hi, Sinclair,

When you wrote:
I could easily solve this problem if the question would not include the 10 ft.

You meant to write: I see that the 10-ft fact is irrelevant but I don't have the courage to say so.

You did, no doubt, work out:
s       5
---- = ----
s+x     15

and dx/dt = -5.

3s = s + x,
2s = x,

2 ds/dt = dx/dt

ds/dt = (dx/dt)/2 = 5/2.

and you didn't need the 10.

Note: The archives in the calculus section contain many examples of related rates exercises.  Look through them.
Choose BROWSE PAST ANSWERS from the menu. Find Calculus and then look for Related Rates in the subject lines.