Question

Optimization Problem:

A man on an island is 4 km from the shore. He wants to go to a pub which is 8 km down the shore. He can row at 3km/h and walk at 5 km/h. Where should he land if he wants to reach the pub as soon as possible?

How can I start this?

Answer 1

Draw a picture and make some triangles. Make some equations that you know to be true, even if they seem simple or stupid. These usually tend to end up being using simple formulas like perimeter or d=rt kind of things you learned as a kid.

Answer 2

well,, I kinda did that.. here's what I got so far..

Answer 3

So let's think about this for a second, don't think in terms of constraints, etc... Ask yourself, what is important to this guy? Does he want to get to the bar while covering the shortest distance? Does he want to do it as fast as possible? What's really going on here?

Answer 4

I think the man just wanted to go to his destination as fast as possible..
which means that he should cover a shorter distance to go to the place in a minimum time..??

Answer 5

List out the things you know with units and give them all variable names, it'll make your life easier. You're given the rate of travel on land and in water, and the distance he is away on land and water. So I'd say:

Rw = 3 km/h
Rl = 5 km/h
Dw = 4 km
Dl = 8 km

Answer 6

He wants to get there as fast as possible, so we want the shortest time, not the shortest distance. See, if he goes the shortest physical distance, it's not the fastest since he walks much faster than he rows. So he needs to get out of the water rather than just follow the hypotenuse straight for the pub. This is where you have a misconception.

Answer 7

oohhh.. ok

Answer 8

For example, suppose you're on the other side of a mountain. The shortest distance might be for me to walk through the mountain, but tunnelling through a mountain takes much longer than hiking around it haha.

Answer 9

So now you see why this is the hypothetical line you need to draw for your path: