Machine A can complete a certain job in x hours. Machine B can complete the same job in y hours. If A and B work together at their respective rates to complete the job, which of the following represents the fraction of the job that B will not have to complete because of A's help?A) (x – y)/(x + y)B) x/(y – x)C) (x + y)/(xy)D) y/(x – y)E) y/(x + y)

Answer:[tex]\frac{y}{x+y}[/tex]Step-by-step explanation:The required answer is the rate at  which Machine A  works when the two machines are combined.Note: the rate of doing work is express as [tex]rate=\frac{1}{time taken} \\[/tex]Hence we can conclude that Machine A working rate is [tex]machine A=\frac{1}{x} \\[/tex] and machine B working rate is [tex]machine B=\frac{1}{y} \\[/tex]When the two machine works together, the effective working rate is [tex]\frac{1}{x}+\frac{1}{y}\\\frac{xy}{x+y}\\[/tex]The fraction of the work that Machine B will not have complete because of Machine A help is the total work done by machine A Hence the fraction of work done by A is expressed as [tex]\frac{1}{x}*combine working rate[/tex][tex]\frac{1}{x}*\frac{xy}{x+y}\\\frac{y}{x+y} \\[/tex]Hence the fraction of the work that Machine B will not have complete because of Machine A help is the total work done by machine A is [tex]\frac{y}{x+y} \\[/tex]