Originally posted by prosoccer
sqrt (distance between boats)^2 + y^2
Do you mean sqrt of that whole expression?
That won't work. Here's a simple case that demonstrates why your expression cannot be an upper bound:
Suppose that the beach ball lies along an extension of the line connecting boat 3 to boat 2. Then the distance between the ball and boat three is equal to [(distance between boats) + y]. It should be fairly clear that this value is strictly greater than the value sqrt[(distance between boats)^2 + y^2].* This is a case which is consistent as a possibility with the information given, so your answer cannot be correct.
*Suppose the distance between boats is a. Then sqrt[a^2 + y^2] < sqrt[a^2 + 2ay + y^2] = sqrt[(a + y)^2] = a + y.
By the way, I'm looking for an answer that just includes specified distances x and y. The question only really makes sense in a context in which x and y are some fixed distances (that can constrain the possible size of the triangle formed by the boats).