Work,

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goyalsau: Legendary Member; Posts: 866; Joined: Mon Aug 02, 2010 6:46 pm; Location: Gwalior, India; Thanked: 31 times

by goyalsau » Fri Nov 19, 2010 11:29 am

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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Source: Beat The GMAT — Problem Solving | Fri Nov 19, 2010 11:29 am

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Rahul@gurome: GMAT Instructor; Posts: 1179; Joined: Sun Apr 11, 2010 9:07 pmFollowed by: 88 members; Location: Milpitas, CA; Thanked: 447 times

by Rahul@gurome » Fri Nov 19, 2010 11:56 am

goyalsau 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 the man = (3/3.5) man-hours = 6/7 man-hours/hour
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
â‰ˆ 20 hours

Therefore it will take approximately 20 hours to complete the work for the three.

Rahul Lakhani
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On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
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goyalsau: Legendary Member; Posts: 866; Joined: Mon Aug 02, 2010 6:46 pm; Location: Gwalior, India; Thanked: 31 times

by goyalsau » Fri Nov 19, 2010 8:01 pm

Rahul@gurome wrote:
goyalsau 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 the man = (3/3.5) man-hours = 6/7 man-hours/hour
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
â‰ˆ 20 hours

Therefore it will take approximately 20 hours to complete the work for the three.

Thanks Rahul,

Saurabh Goyal
[email protected]
-------------------------

EveryBody Wants to Win But Nobody wants to prepare for Win.

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RikaMueller: Junior | Next Rank: 30 Posts; Posts: 19; Joined: Fri Jul 16, 2010 1:27 am

by RikaMueller » Sat Nov 20, 2010 2:51 am

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

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Rahul@gurome: GMAT Instructor; Posts: 1179; Joined: Sun Apr 11, 2010 9:07 pmFollowed by: 88 members; Location: Milpitas, CA; Thanked: 447 times

by Rahul@gurome » Sat Nov 20, 2010 3:16 am

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

The man works for 3 hours and then takes rest for 0.5 hour.
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.

Rahul Lakhani
Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
+91-99201 32411 (India)

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