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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)

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olasunkanmilesanmi

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]

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