1. ## Related Rates help

Hi I am in the middle of solving this provlem however, since I am only given a limited amount of information I am confused as to how to solve it.

"Two cars start moving from teh same point. One travels south at 60 mi/h and the other travels west at 25 mi/h. At what rate is the distance between the cars increasing two hours later?"

So far I have the equation..
(z^2) = (x^2) + (y^2)

I know dy/dt = 60 mi/h and dx/dt = 25 mi/h.

I implicity differentiated the first equation and ended up with:
dz/dt = (50x +120y)*(1/2z)

Since I do not know what x or y is I am unable to find the rate the distance between the two cars is increasing.

Thank you so much for your help!

2. Originally Posted by aquaglass88
Hi I am in the middle of solving this provlem however, since I am only given a limited amount of information I am confused as to how to solve it.

"Two cars start moving from teh same point. One travels south at 60 mi/h and the other travels west at 25 mi/h. At what rate is the distance between the cars increasing two hours later?"

So far I have the equation..
(z^2) = (x^2) + (y^2)

I know dy/dt = 60 mi/h and dx/dt = 25 mi/h.

I implicity differentiated the first equation and ended up with:
dz/dt = (50x +120y)*(1/2z)

Since I do not know what x or y is I am unable to find the rate the distance between the two cars is increasing.

Thank you so much for your help!
Two hours later, the one car is 120 miles south (y = 120), and the other car is 50 miles west (x = 50).

$\displaystyle z^2 = 120^2+50^2$

Plug x, y, and z into your dz/dt equation.

3. Oh ok I understand now! thank you so much!

4. Originally Posted by aquaglass88
Oh ok I understand now! thank you so much!
You are welcome AquaGlass!