Question 277233: The company newsletter needs to get out by the end of the workday. Karen can staple and fold all of the newsletters in 23 hours. John could do it by himself in 17 hours. Mary could do it by herself in 19 hours.
Karen begins to work, then one hour later Mary joins her, then two hours after that, John joins them. If Karen began stapling and folding at 8:00, will the job be done by 5:00? How long would each person have been working by the time the job is done?
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website! The company newsletter needs to get out by the end of the workday. Karen can staple and fold all of the newsletters in 23 hours. John could do it by himself in 17 hours. Mary could do it by herself in 19 hours.
Karen begins to work, then one hour later Mary joins her, then two hours after that, John joins them. If Karen began stapling and folding at 8:00, will the job be done by 5:00? How long would each person have been working by the time the job is done?
The problem has to be done in 3 steps.
work out how much work karen does alone in 1 hour. Calculate the balance
work out how much job Karen and Mary together do for 2 hours till john joins. Find the balance job .
Find how much time all three take to finish the remaining job .
Karen takes 23 hours to do the job. She doe 0.043 part of job in 1 hour
Karen and Mary do 1/23 + 1/19 of the job in 1 hour = 0.096 part in 1 hour
Karen Mary & john do 1/23 + 1/19 +1/17 job in 1hour = 0.155 part in 1 hour
Karen has finished 0.043 job when Mary joins her. Balance remaining 0.957
Karen & Mary do 0.096 job in hour. in 2 hours they do 2*0.096= 0.192 job.
Balance remaining 0.957-0.192= 0.765
All three do 0.155 job in 1 hour. to complete balance 0,765 of the job they work for 0.765/0.155 = 4.93 hours say about 3 hours
The job is finished in 3+2 +1 = 6 hours
John works for 3 hours
Mary works for 3+2 hours = 5
Karen works for 3+2+1= 6 hours.
So by 2 pm they finish.
Cheers
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