Working simultaneously at their respective constant rates, Machines \(A\) and \(B\) produce \(800\) nails in \(x\) hours

Working simultaneously at their respective constant rates, Machines \(A\) and \(B\) produce \(800\) nails in \(x\) hours. Working alone at its constant rate, Machine \(A\) produces \(800\) nails in \(y\) hours. In terms of \(x\) and \(y,\) how many hours does it take Machine \(B,\) working alone at its constant rate, to produce \(800\) nails?

(A) \(\dfrac{x}{x+y}\)

(B) \(\dfrac{y}{x+y}\)

(C) \(\dfrac{xy}{x+y}\)

(D) \(\dfrac{xy}{x-y}\)

(E) \(\dfrac{xy}{y-x}\)

Answer: E

Source: Official Guide