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

Question

anonymous · Answer

This is tricky: I draw a diagram to solve these problems - in the boat you are going to rowalong the hypotenuse of a triangle some distance d=(2^2+x^2)^0.5 and land on the coast x mi towards goal. this leaves jane 5-x miles to walk to her village. The trip takes:
$$T=2*\sqrt{x^2+2^2}+5*(5-x)$$
This can be solved by differentiating and setting T=0 to find the optimum value of x.
It is about 0.87 and give a time of 1 hour 55, just under the 2 hours it would take if she just rowed straight to shore and walked.