Two cars are approaching an intersection.

Two cars are approaching an intersection. One is 2 miles south of the intersection and is moving at a constant speed of 30 miles per hour. At the same time, the other car is 3 miles east of the intersection and is moving at a constant speed of 40 miles per hour.

a) Express the distance d between the cars as a function of time t.
[Hint: at t = 0, the cars are 2 miles south and 3 miles east of the intersection, respectively.

b) Use a graphing utility to graph d = d (t). For what value of t is d smallest?

Answers:
a) d (t) = √2500t^2 – 360t + 13
b) d is smallest when t = 0.072 hr.

I just need help with the A part. The B part is easily. I have a hard time setting up my f(x) part. I am not sure the answers are right in the book on this one I keep on getting something diffrent as my d(t).

I got it... was reworking it today and had my numbers backwards..

here how you get part a)

(2-30t)² + (3-40t)²

(4 - 120t + 900t²) + (9 - 240t + 1600t²)

d(x) = √2500t² - 360t +13

Now take the derivative and set equal to zero to find the min.