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Question 54597: Amy can do a certain job task in 4 hours. She decided to help her brother Jim after he spent 2 hours on the task. Together they finished the task in 2 more hours.
a)how long would it take for jim to do the task on his own?
b)how long would it take for them to do it together if Amy had joined jim from the beginning?
Answer by venugopalramana(3286)   (Show Source):
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It takes 5 hours for John to do some job.
JOHN IN 1 HR DOES 1/5=0.2 JOB
he worked for an hour ,
HENCE JOHN COMPLETED 1/5 JOB....
BALANCE JOB = 1-1/5 = 4/5=0.8 JOB
and then Mike joined . Together they finished the job in 1 1/2 hour.
THAT IS JOHN + MIKE TOOK 1.5 HRS TO DO 4/5=0.8 JOB
JOHN+MIKE DO IN 1 HR 0.8/1.5=8/15 JOB
BUT JOHN DOES IN 1 HR 1/5 JOB
SO MIKE DID IN 1 HR .....8/15 - 1/5 = 5/15=1/3 JOB
SO MIKE NEEDS 1/(1/3) HRS = 3 HRS TO DO 1 WHOLE JOB.
a) how long would it take mike to do the job by himself?
SO MIKE NEEDS 1/(1/3) HRS = 3 HRS TO DO 1 WHOLE JOB.
b) if john worked for 3 hours before mike joined him , how long would it take for them to finish the job together?
JOHN DOES IN 3 HRS 3/5 JOB
BALANCE JOB =1-3/5 = 2/5 JOB
JOHN + MIKE DO IN 1 HR 8/15 JOB
JOHN + MIKE NEED (2/5)/(8/15)=(2*15)/(8*5) = 3/4 HRS TO COMPLETE THE JOB
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