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GMAT - Problem Solving - Time and Work

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 alon

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) x/(x y) 
(B) y/(x y) 
(C) xy/(x y) 
(D) xy/(x-y) 
(E) xy/(y-x)

Assume the time taken by B to produce 800 nails be k

Rate at which B produces nails = 800/k

Rate at which A produces nails = Number of nails produced / time taken = 800/y

Combined rate = 800/k + 800/y
Combined time taken for production of 800 nails = x = 800 / (800/k + 800/y)

Simplifying,

1/k + 1/y = 1/x

1/k = 1/x - 1/y = (y - x)/xy

k = xy / (y - x)

Ans. xy / (y - x)

E.