Optimization problem, just wanting my work checked


New member
Oct 19, 2020
Hello, I have completed the following problem, and I am wondering if an expert would like to review what I have done and scan it for any flaws, because I am unsure of myself as a mathematician.

Gary is aboard a ship that is 4.7miles away from the coast. His destination is a village that is 8.9 miles further down the coast. He is able to row at 2.3 miles per hour, and is able to walk at a rate of 3.75 miles per hour.

1. Where on the coast should Gary land on the coast that will save him the most time in reaching the village?
2. What is the least possible amount of time it will take Gary to reach the village?

First I drew a picture in mspaint to help me:

I begin with the Pythagorean theorem to calculate the side of this triangle:

To find the least possible time, I plugged 3.65 into my time optimization function and got an answer of: 3.987.

Personally, I think Gary would have been there a lot sooner if he had just started rowing instead of doing math.