A man is sitting in a lake in his boat fishing when he receives a call on his cell phone. A barbecue is happening a ways down the shoreline, and he had better get there fast so as not to miss out. He is two miles out perpendicular to the shore, and 7 miles horizontally from the location on the beach from the barbecue. If the lake has no current and the wind is negligible, he can row toward the shoreline at a rate of 3 mph. When he reaches dry land, he can run at 5 miles per hour. If he wants to reach the barbecue as quickly as possible, how far horizontally should he land the boat from his current location?
As a bonus, if we assign the distance from the shore to be A miles, the distance from the barbecue along the shoreline B miles, and the boat speed and running speed C and D miles per hour respectively, does there exist a function that will output the ideal place to land the boat for all positive values of A,B,C, and D? If so, what is it? If not, why not?
The official solution that has been posted to this problem is poorly constructed. In fact, it is blatantly incorrect. And to top it all off, it talks about 'deriving' a function. AARGGH!! You don't 'derive' a function, you 'DIFFERENTIATE' it!!! These two words are NOT interchangeable!
I apologise for speaking so strongly about this... but good grief! Don't we have Journeymen (or somebody) proofreading these things before they get posted?
For a good solution, see the previous post by Bractals. Incidentally, it seems to me that it may indeed be possible for us to find a function that works for all positive values of A, B, C and D - but it will probably have to be piecewise defined. Anyone care to provide it?
-John
I hate to be a downer, but...
