# Math Help - Optimization problem (not sure if I understand correctly)

1. ## Optimization problem (not sure if I understand correctly)

A man in a boat is 3 km offshore and wishes to go to a point on the shore that is 5km from the point that is directly opposite his present position. The man can walk at 4 km/h and row at 2 km/h. At what point should he land so as to reach his destination in the shortest time? What is the traveling time?

I set up the equation as follow $\displaystyle d(t)=\sqrt{(3-2t)^2 + (5-4t)^2}$

Differentiating and found a local minimum at $x=\frac{10}{13}$

However, the answer in supposedly 3.27 km, 2.55 hours.

What am I doing wrong?

2. Originally Posted by youngb11
A man in a boat is 3 km offshore and wishes to go to a point on the shore that is 5km from the point that is directly opposite his present position. The man can walk at 4 km/h and row at 2 km/h. At what point should he land so as to reach his destination in the shortest time? What is the traveling time?

I set up the equation as follow $\displaystyle d(t)=\sqrt{(3-2t)^2 + (5-4t)^2}$

Differentiating and found a local minimum at $x=\frac{10}{13}$

However, the answer in supposedly 3.27 km, 2.55 hours.

What am I doing wrong?
did you make a sketch?

first off, you're minimizing time.

$time = \frac{distance}{speed}$

$t_{total} = \dfrac{\sqrt{x^2+9}}{2} + \dfrac{5-x}{4}$

set $\dfrac{dt}{dx} = 0$ and find the value of $x$ that minimizes $t$.

btw ... don't bump.

3. Originally Posted by skeeter
did you make a sketch?

first off, you're minimizing time
Ahh, that's what I was missing. Thanks a lot for your help!

Sorry about the bumping, won't happen again.