Question

Working together, machine J, machine K, and machine L can complete a job in 12 minutes. Working alone, machine J can complete a job in 20 minutes. Machine J worked alone for a given amount of time. Then, machines K and L worked together, and with no other machine, for the same amount of time. How long the total time required?

Answer 1

Total required time is 24 minutes.

Explanation:

It is given that working together, machine J, machine K, and machine L can complete a job in 12 minutes.

Part of job completed by all machines together in one minute is

One minute work of all =
`(1)/(12)`

Working alone, machine J can complete a job in 20 minutes.

Part of job completed by machine J in one minute =
`(1)/(20)`

Part of job completed by machine K and L together in one minute is

One minute work of K and L together =
`(1)/(12)-(1)/(20)=(1)/(30)`

It is given that Machine J worked alone for a given amount of time. Then, machines K and L worked together, and with no other machine, for the same amount of time.

Let the given amount of time be x.

`(1)/(20)x+(1)/(30)x=1`

`(1)/(12)x=1`

Multiply both sides by 12.

`x=12`

Total required time is

`2x=24`

Therefore total required time is 24 minutes.