Work-related Problems

 

Case 1: Workers have different rates

Work rate × Time to finish the job = 1 job done

Work rate = (1 job done) / (Time to finish the job)

Time of doing the job = (1 job done) / (Work rate)

 

For example
Albert can finish a job in A days
Bryan can finish the same job in B days
Carlo can undo the job in C days
 

1/A = rate of Albert
1/B = rate of Bryan
1/C = rate of Carlo
 

Albert and Bryan work together until the job is done: (1/A + 1/B)t = 1
Albert is doing the job while Carlo is undoing it until the job is done: (1/A - 1/C)t = 1
 

Problem
Lejon can finish a job in 6 hours while Romel can do the same job in 3 hours. Working together, how many hours can they finish the job?

Solution

 

Case 2: Workers have equal rates

Work load = no. of workers × time to finish the job

Work done = no. of workers × time of doing the job

 

To finish the job

Work done = Work load

 

If a job can be done by 10 workers in 5 hours, the work load is 10(5) = 50 man-hours. If 4 workers is doing the job for 6 hours, the work done is 4(6) = 24 man-hours. A remaining of 50 - 24 = 26 man-hours of work still needs to be done.
 

Problem
Eleven men could finish the job in 15 days. Five men started the job and four men were added at the beginning of the sixth day. How many days will it take them to finish the job?
 

Solution

 

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