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ruslelena [56]
3 years ago
9

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 the

ir 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)
Mathematics
1 answer:
scZoUnD [109]3 years ago
6 0

Answer:

\frac{y}{x+y}

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

rate=\frac{1}{time taken} \\

Hence we can conclude that Machine A working rate is

machine A=\frac{1}{x} \\ and machine B working rate is

machine B=\frac{1}{y} \\

When the two machine works together, the effective working rate is

\frac{1}{x}+\frac{1}{y}\\\frac{xy}{x+y}\\

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

\frac{1}{x}*combine working rate

\frac{1}{x}*\frac{xy}{x+y}\\\frac{y}{x+y} \\

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 \frac{y}{x+y} \\

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Below.

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