# Another optimization problem assistance

• April 4th 2011, 04:45 PM
IanCarney
Another optimization problem assistance
At 2:30 pm, Bob heads north from an intersection at 120 km/h. Alvin is driving east at 96 km/h and reaches the same destination at 5:10 pm. When are they closest to each other.

$d(t)=\sqrt{(120t)^2+(256-96t)^2}$

Is that correct? The answer is supposedly 3:32 PM, so I'm not sure if I understood it incorrectly or if the book had a typo.

Thanks for the assistance!
• April 4th 2011, 05:04 PM
skeeter
t = 0 at 2:30

minimizing the quantity $(120t)^2 + (256-96t)^2$ will also minimize it's square root.

book is correct.
• April 4th 2011, 05:07 PM
IanCarney
Quote:

Originally Posted by skeeter
t = 0 at 2:30

minimizing the quantity $(120t)^2 + (256-96t)^2$ will also minimize it's square root.

book is correct.

Ah, thanks! Missed that.