# Thread: Need help setting up Optimization problem

1. ## Need help setting up Optimization problem

Any hints on how to set up the function for this problem?

A boat leaves a dock at 2:00 pm and travels due south at a speed of 20 km/hr. Another boat has been heading due east at 15 km/hr and reaches the same dock at 3:00 pm. At what time were the two boats closest together?

From the question, I know that I have to minimize the distance between the boats, which can be obtained using the pythagorean theorem or distance formula. But that's about all I can think of.
Anyone have any idea on how to set the equation using those speeds?

2. Originally Posted by Arturo_026
Any hints on how to set up the function for this problem?

A boat leaves a dock at 2:00 pm and travels due south at a speed of 20 km/hr. Another boat has been heading due east at 15 km/hr and reaches the same dock at 3:00 pm. At what time were the two boats closest together?

From the question, I know that I have to minimize the distance between the boats, which can be obtained using the pythagorean theorem or distance formula. But that's about all I can think of.
Anyone have any idea on how to set the equation using those speeds?

let t = 0 be 2:00 PM and the port be the origin

1st boat position ...

$y = -20t$

2nd boat position ...

$x = -15 + 15t$

let $r$ = distance between the two positions at any time $t$ ...

$r^2 = (-20t)^2 + (-15+15t)^2$

minimize $r^2$ w/r to time and you minimize $r$

3. Ok, I get t=9/25 as the time when the boats are closer, but since the time goes from 2:00 pm to 3:00 pm, do I subtract those 21 min. 35 sec. from 3:00 or add them to 2:00?

4. Originally Posted by Arturo_026
Ok, I get t=9/25 as the time when the boats are closer, but since the time goes from 2:00 pm to 3:00 pm, do I subtract those 21 min. 35 sec. from 3:00 or add them to 2:00?
t = 0 is 2:00 PM

what does that tell you?