It takes John 4 hours to do a job, it takes Kate 3 hours to do the same job, and it takes Nathan 2 hours. How long will it take if they all work together.

Question

Need to know how much time it would take for them to finish the job, working as a team. In the fraction form.

Answer 1

John 4 hours to do a job ... 1/4 job per hour

Kate 3 hours ... 1/3 job per hour

Nathan 2 hours ... 1/2 job per hour

 

Together they perform

1/4 + 1/3 + 1/2 = 3/12 + 4/12 + 6/12 = 13/12 job per hour.

 

This means the total job is complete in LESS than an hour.

 

(13/12 job/hour)(h hours) = 1 job

 

h = 12/13 of an hour to do the job together

 

(12/13 hours)(60 minutes/hour) = 55 5/13 minutes

 

(5/13 minutes)(60 seconds/minute) = 23.08 seconds

 

If you wish to take it that far then, all things being equal,

it takes the 3 of them a total of 55 minutes 23.08 seconds