Optimization problem, just wanting my work checked

[mickey222]

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.

 

[Otis]

… I have completed the following problem … would like [someone] to review what I have done and scan it for any flaws …

Hi mickey. Your reasoning and calculations look correct, although we wouldn't report the time to the nearest thousandth of an hour because none of the given measurements are that precise. Some of your wording and symbolism could be improved, but that's secondary. (Instructors will understand what you intended to say.) I think you did a good job, overall.

I like to see answers to word problems reported with units, and I think complete sentences are good form, too.

EG:

"Gary ought to land at a point roughly 3.65 miles north of the village."

"The minimum trip time is about 4 hours."

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

Ha -- that is funny. Of course, technically speaking, Gary didn't need to do any math because Gary wasn't asked to minimize his trip time. You were.