Thread: 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

Differentiating and found a local minimum at

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

What am I doing wrong?

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

Differentiating and found a local minimum at

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.





set and find the value of that minimizes .


btw ... don't bump.

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.