Related Rates - A Distance Problem (Calculus)

If Nick is moving north at 4m per second, and Sarah is moving south at 2m per second, how fast will the distance between them be changing after 30 seconds?

Learn how to tackle this problem as well as a basic strategy for all related rates problems in this video!

Please leave questions in the comments!

[Ensign_Cthulhu]

0:30 The problem is ambiguously worded with regard to the starting position. As you have constructed it, it implies that the separation is purely lateral (i.e. at time zero they are exactly east/west of each other), but this is not explicitly stated in the problem.

[Generatorman]

If I were working this problem, I would have been stuck before you took the derivative.  I would have known that (x+y)^2 was (180m)^2.  So, I would have written (180m)^2 + (150m)^2 = Z^2. What guidelines would you suggest I use so I don't get tripped up on these types of problems?

[johnnolen]

Pardon me for pointing this out but your final answer is incorrect. The true result is z' = 4.609 m/s. You evidently made a transposition error when you typed the value of z into your calculator. 180 ÷ 234 = 0.7692. The number you recorded for this calculation was 0.74. When 180 ÷ x = 0.74 then x = 243.