A man can work for three hours non-stop but then needs to take rest for half an hour. His wife can work for two hours but rests for 15 min after that, while his son can work for 1 hour before resting for half an hour. If a work takes 50 man-hours to get completed, then approximately how long will it take for the three to complete the same? Assume all of them all equally skilled in their work.
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- goyalsau
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Effective work rate for the man = (3/3.5) man-hours = 6/7 man-hours/hourgoyalsau wrote:A man can work for three hours non-stop but then needs to take rest for half an hour. His wife can work for two hours but rests for 15 min after that, while his son can work for 1 hour before resting for half an hour. If a work takes 50 man-hours to get completed, then approximately how long will it take for the three to complete the same? Assume all of them all equally skilled in their work.
Effective work rate for his wife = (2/2.25) man-hours = 8/9 man-hours/hour
Effective work rate for his son = (1/1.5) man-hours = 2/3 man-hours/hour
Total work rate of the three = (6/7 + 8/9 + 2/3) man-hours/hour = 152/63 man-hours/hour
The work requires = 50 man-hours
If they work together total time required = (50 man-hours)/Total work rate
= (50)/(152/63) hours
= (50*63)/152 hours
≈ 20 hours
Therefore it will take approximately 20 hours to complete the work for the three.
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- goyalsau
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Thanks Rahul,Rahul@gurome wrote:Effective work rate for the man = (3/3.5) man-hours = 6/7 man-hours/hourgoyalsau wrote:A man can work for three hours non-stop but then needs to take rest for half an hour. His wife can work for two hours but rests for 15 min after that, while his son can work for 1 hour before resting for half an hour. If a work takes 50 man-hours to get completed, then approximately how long will it take for the three to complete the same? Assume all of them all equally skilled in their work.
Effective work rate for his wife = (2/2.25) man-hours = 8/9 man-hours/hour
Effective work rate for his son = (1/1.5) man-hours = 2/3 man-hours/hour
Total work rate of the three = (6/7 + 8/9 + 2/3) man-hours/hour = 152/63 man-hours/hour
The work requires = 50 man-hours
If they work together total time required = (50 man-hours)/Total work rate
= (50)/(152/63) hours
= (50*63)/152 hours
≈ 20 hours
Therefore it will take approximately 20 hours to complete the work for the three.
Saurabh Goyal
[email protected]
-------------------------
EveryBody Wants to Win But Nobody wants to prepare for Win.
[email protected]
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Hi Rahul,
can you just shortly explain how you arrive at eg: 3/3.5. Is it 3.5 hrs total which the man needs into 3?
Thanks
can you just shortly explain how you arrive at eg: 3/3.5. Is it 3.5 hrs total which the man needs into 3?
Thanks
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- Rahul@gurome
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The man works for 3 hours and then takes rest for 0.5 hour.RikaMueller wrote:Hi Rahul,
can you just shortly explain how you arrive at eg: 3/3.5. Is it 3.5 hrs total which the man needs into 3?
Thanks
Thus effectively the man does 3 man-hours of work in 3.5 hours.
=> Work rate of the man = (3 man-hours)/(3.5 hours) = (3/3.5) man-hours/hour
Hope it is clear now.
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Quant Expert
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