Work Problem

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garuhape: Senior | Next Rank: 100 Posts; Posts: 74; Joined: Fri Dec 17, 2010 12:37 pm; Location: Munich; Thanked: 3 times

by garuhape » Mon Mar 21, 2011 4:35 am

The ratio of the rates of Bob, John and Craig is 1 to 2 to 5 respectively, if the three work together on the project it takes 4 hours to complete. How long does it take John to do the job alone?

Can someone explain please why the OA is 16 and noch 32!

Thx

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Source: Beat The GMAT — Problem Solving | Mon Mar 21, 2011 4:35 am

Night reader: Legendary Member; Posts: 1337; Joined: Sat Dec 27, 2008 6:29 pmFollowed by: 10 members; Thanked: 127 times

by Night reader » Mon Mar 21, 2011 5:02 am

let us call Bob's work =b, John's =j, Craig's =c. The ratio is b:j:c=1:2:5. The work performed b + j + c = 1/4. Find j-?
b/j=1/2 OR b=j/2
j/c=2/5 OR c=5j/2 --> b + j + c = 1/4 <> j/2 + j + 5j/2 =1/4. By solving for j we get, 2j+4j+10j=1, 16j=1, j=1/16

1 is work and 16 is time; above rate/speed --> b + j + c = 1/4 <-- work/time OR 1/4

garuhape wrote:The ratio of the rates of Bob, John and Craig is 1 to 2 to 5 respectively, if the three work together on the project it takes 4 hours to complete. How long does it take John to do the job alone?

Can someone explain please why the OA is 16 and noch 32!

Thx

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Geva@EconomistGMAT: GMAT Instructor; Posts: 905; Joined: Sun Sep 12, 2010 1:38 amFollowed by: 123 members; Thanked: 378 times; GMAT Score:760

by Geva@EconomistGMAT » Mon Mar 21, 2011 5:04 am

garuhape wrote:The ratio of the rates of Bob, John and Craig is 1 to 2 to 5 respectively, if the three work together on the project it takes 4 hours to complete. How long does it take John to do the job alone?

Can someone explain please why the OA is 16 and noch 32!

Thx

the short answer is because John has a rate of 2, not 1.

the long answer is because ou're working with fractions, and not real numbers. Use actual things you can visualize the problem around. Let's say that our heroes's rates are given in actual things: tables/hour, so that John makes Bob makes 1 table an hour, John makes 2 tables an hour, and Craig makes 5 tables an hour.

together, our heroes work at a rate of 1+2+5 = 8 tables an hour. After four hours, they make 4*8=32 tables - that's the work.
At a rate of 2 tables an hour, how long will it take John to do 32 tables alone?
32/2 = 16 hours.

Geva
Senior Instructor
Master GMAT
1-888-780-GMAT
https://www.mastergmat.com

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force5: Legendary Member; Posts: 582; Joined: Tue Mar 08, 2011 12:48 amFollowed by: 6 members; Thanked: 61 times; GMAT Score:740

by force5 » Mon Mar 21, 2011 7:31 am

well said Geva..

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