SOLUTION: A man can do a job in 8 hours, a boy can do the same job in 12 hours and a girl can do it in 16 hours. How long will it take them to do the job if the man and the boy work together
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Question 1159402: A man can do a job in 8 hours, a boy can do the same job in 12 hours and a girl can do it in 16 hours. How long will it take them to do the job if the man and the boy work together for one hour and then the boy and the girl finish the job? Found 2 solutions by mananth, Theo:Answer by mananth(16946) (Show Source):
You can put this solution on YOUR website! A man can do a job in 8 hours, he does 1/8 of the job in 1 hour
a boy can do the same job in 12 hours, he does 1/12 of the job in 1 hour
and a girl can do it in 16 hours She he does 1/16 of the job in 1 hour
the man and the boy work together for one hour
So they do 1/8 +1/12 of the job = 5/24 of the job
Balance job = 1- (5/24 ) = 19/24
and then the boy and the girl finish the job?
boy and girl together do (1/12 + 1/16) of the job in 1 hour = 7/48
7/48 of job 1 hour
19/24 of the job in t hours = (19/24)/(7/48) = 5.4 hours
Total 5.4 + 1 = 6.4 hours
man rate is 1/8 of the job in 1 hour.
boy rate is 1/12 of the job in 1 hour.
girl rate is 1/16 of the job in 1 hour.
when they work together, their rates are additive.
for the man and the boy, the combined rate becomes 1/8 + 1/12 = 3/24 + 2/24 = 5/24.
for the boy and the girl, the combined rate becomes 1/12 + 1/16 = 4/48 + 3/48 = 7/48.
the combined rate for the man and the boy is 5/24 = 10/48.
the combined rate for the boy and the girl is 7/48.
the man and the boy work together for 1 hour.
the formula becomes 10/48 * 1 = q
solve for q to get q = 10/48
since the total job is equal to 1, you get 1 - 10/48 = 48/48 - 10/48 = 38/48 of the job still needs to be done.
the boy and the girl work for t hours to finish the job.
the formula becomes 7/48 * t = 38/48
solve for t to get t = 38/48 * 48/7 = 38/7 hours.
the man and the boy work for 1 hour.
the boy and the girl work for 38/7 hours.
the total time spent on the job is 1 + 38/7 = 7/7 + 38/7 = 45/7 hours.
to confirm, add the two formulas together to get:
r * t for man and boy equals 10/48 * 1 = 10/48 of the job.
r * t for boy and girl equals 7/48 * 38/7 = 38/48 of the job.
10/48 + 38/48 = 48/48 = the whole job.
your solution is that the total time to complete the job was 1 + 38/7 = 7/7 + 38/7 = 45/7 hours.
the decimal equivalent of that is 6.428571429 hours.
i'll be available to answer any questions you might have about this.
