# Diffrential calculus; distance problem

1. Dec 8, 2007

### jnimagine

1. The problem statement, all variables and given/known data
Two cars approach an intersection at the same time. The red car is 300m east of the intersection and traveling at a speed of 60km/h. The blue car is 450m north of the intersection and traveling at a speed of 75km/h. When are the two cars the closest?

2. Relevant equations
c^2 = a^2 + b^2

3. The attempt at a solution

I converted the speeds into m/s first then used it in a pythagorean theorem equation and found the derivative.
75km/h = 20.8m/s 60km/h = 16.7m/s
c^2 = (20.8t - 450)^2 + (16.7t - 300)^2
and when i do the derivative i get 20.2. But I was just wondering, does it make a difference whether i do 20.8t - 450 or 450 - 20.8t??

2. Dec 8, 2007

### HallsofIvy

Staff Emeritus
Here it doesn't matter because of the squares. 20.8t- 450 is the negative of 450- 20.8t but squaring removes the difference.

But you get "20.2" for what? This problem asks when the two cars will be closest. That requires a time answer. If you mean "The two cars will be closest 20.2 seconds after the starting time (when they are at the given positions)", you must include the "seconds".