Question

two cars are approaching an intersection one is 3 miles south of the intersection and is moving at a constant speed of 20 miles per hour. at the same time the other car is 4 miles east of the intersection and is moving at the constant speed of 30 miles per hour.

a)express the distance d as a function of time t.
b)Use a graphing utility to graph d=d(t). For what value of t is d​ smallest?

Answer 1

At a time of t hours after the action started,

- distance remaining for the northbound car before reaching intersection is 3 - 20t
- distance remaining for the westbound car before reaching the intersection is 4 - 30t

let d be the distance between them
d^2= (3-20t)^2 + (4-30t)^2
= 9 - 120t + 400t^2 + 16 - 240t + 900t^2
= 1300t^2 - 360t + 25

I have no idea what "graphing utility " you are using.
for a min of d , dd/dt = 0
2d dd/dt = 2600t - 360
2600t = 360
t = .13846... hrs