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

Answer:

Total required time is 24 minutes.

Step-by-step 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 = $\frac{1}{12}$

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

Part of job completed by machine J in one minute = $\frac{1}{20}$

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

One minute work of K and L together = $\frac{1}{12}-\frac{1}{20}=\frac{1}{30}$

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.

$\frac{1}{20}x+\frac{1}{30}x=1$

$\frac{1}{12}x=1$

Multiply both sides by 12.

$x=12$

Total required time is

$2x=24$

Therefore total required time is 24 minutes.