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)

Answer: E. [tex]\dfrac{xy}{y-x}[/tex]Step-by-step explanation:Given : Working simultaneously at their respective constant rates, Machines A and B produce 800 nails in x hours.Taking whole job as 1.The rate of Machines A and B working together = [tex]\dfrac{1}{x}[/tex]Working alone at its constant rate, Machine A produces 800 nails in y hours. The rate of work by Machines A = [tex]\dfrac{1}{y}[/tex]Let t be the time taken by Machine B to complete the whole work .The rate of  work by Machines B will be :-[tex]\dfrac{1}{t}=\dfrac{1}{x}-\dfrac{1}{y}\\\\\Rightarrow\ \dfrac{1}{t}=\dfrac{y-x}{xy}\\\\\Rightarrow\ t= \dfrac{xy}{y-x}[/tex]Hence, the expression for hours taken by Machine B, working alone at its constant rate, to produce 800 nails : [tex]\dfrac{xy}{y-x}[/tex]