# Math Help - [SOLVED] Application of Differentiation

1. ## [SOLVED] Application of Differentiation

Hey guys

Two straight roads intersect at right angles. Two men, A and B, are 100 km from the intersection, one on each road. They drive towards the intersection at 30 km/h and 40 km/h respectively. Find the distance of each driver from the intersection as a function of t, the time in hours for which they are driving. Hence, find their distance apart, d(t), at any time. For what value of t is their distance apart least?

How exactly do I do this question? I don't seem to get it .

2. So sorry!

I solved it after staring at the question for 10 minutes (after i posted it ).

3. ## How did you solve it?

Hi there, mind to share your solution? Thanks!

4. I presume it suddenly occured to you to use the Pythagorean theorem? If t is the time, in hours, after the intial point, then the distance of each to the intersection is 100- 30t and 100- 40t. The straight line distance between them is $D= \sqrt{(100- 30t)^2+ (100- 40t)^2}$.

That will be minimized when $D^2= (100- 30t)^2+ (100- 40t)^2$ is minimized, so you don't have to worry about differentiating the square root.

5. Thanks so much.

So, the next step would be to differentiate D wrt t, equate dD/dt = 0 and find t?
I'm getting weird equations upon calculating t.