# Math Help - Quickest Route

1. ## Quickest Route

Jane is 2 miles offshore in a boat and wishes to reach a coastal village 6 miles down a straight shoreline from the point nearest the boat. She can row 2mph and walk 5mph. Where should she land her boat to reach the village in the least amount of time?

I've never done optimization using time before. Any help is appreciated, thanks.

2. Originally Posted by lancelot854
Jane is 2 miles offshore in a boat and wishes to reach a coastal village 6 miles down a straight shoreline from the point nearest the boat. She can row 2mph and walk 5mph. Where should she land her boat to reach the village in the least amount of time?

I've never done optimization using time before. Any help is appreciated, thanks.
make a sketch.

you want to minimize time ...

time = distance/rate

$\displaystyle t = \frac{\sqrt{2^2 + x^2}}{2} + \frac{6-x}{5}$

find $\frac{dt}{dx}$ and minimize.

3. May I just ask where the 4 came from? Everything else is understandable, thanks for the help.

4. Originally Posted by lancelot854
May I just ask where the 4 came from? Everything else is understandable, thanks for the help.
should be 5 for the speed on land ... my typo.