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 = [tex]\frac{1}{12}[/tex]
Working alone, machine J can complete a job in 20 minutes.
Part of job completed by machine J in one minute = [tex]\frac{1}{20}[/tex]
Part of job completed by machine K and L together in one minute is
One minute work of K and L together = [tex]\frac{1}{12}-\frac{1}{20}=\frac{1}{30}[/tex]
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.
[tex]\frac{1}{20}x+\frac{1}{30}x=1[/tex]
[tex]\frac{1}{12}x=1[/tex]
Multiply both sides by 12.
[tex]x=12[/tex]
Total required time is
[tex]2x=24[/tex]
Therefore total required time is 24 minutes.
