Question

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 1

`(y)/(x+y)`

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=(1)/(time taken) \\`

Hence we can conclude that Machine A working rate is

`machine A=(1)/(x) \\` and machine B working rate is

`machine B=(1)/(y) \\`

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

`(1)/(x)+(1)/(y)\\(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

`(1)/(x)*combine working rate`

`(1)/(x)*(xy)/(x+y)\\(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
`(y)/(x+y) \\`