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# Dan can do a job alone in 15 hours. Fred, working alone, can do the sa

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Math Expert
Joined: 02 Sep 2009
Posts: 59722
Dan can do a job alone in 15 hours. Fred, working alone, can do the sa  [#permalink]

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07 Feb 2016, 10:11
00:00

Difficulty:

5% (low)

Question Stats:

87% (01:19) correct 13% (02:11) wrong based on 119 sessions

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Dan can do a job alone in 15 hours. Fred, working alone, can do the same job in just 10 hours. If Dan works alone for 9 hours and then stops, how many hours will it take Fred, working alone, to complete the job?

A. 4
B. 5
C. 6
D. 12
E. 12.5

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Re: Dan can do a job alone in 15 hours. Fred, working alone, can do the sa  [#permalink]

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08 Feb 2016, 08:31
Here is how a did it:

Work formula = Work = Time x Rate

For Dan: Rate = 1/15
For Fred: Rate = 1/10

Dan works for 9 hours = work = 9 x 1/15 = 9/15 = 3/5 . So Dan does 3/5 of the work in 9 hours.
So Fred must do 1-(3/5)=2/5 of the job in X hours.
1/10xTIME=2/5
TIME=20/5= 4 hours

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Re: Dan can do a job alone in 15 hours. Fred, working alone, can do the sa  [#permalink]

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12 Feb 2016, 10:15
1
So what is the LCM of 15 and 10-----> 30
So we can assume that the total work is 30 units
Dan's Rate is 2units/hr
Fred's Rate is 3 units/hr

So after 9hrs, Dan has done 2*9 = 18 units of work
Remaining work left is 30-18 = 12 units of work

Fred will do 12 units of work in 12/3 = 4hrs
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Joined: 14 Dec 2014
Posts: 18
Concentration: Technology
Re: Dan can do a job alone in 15 hours. Fred, working alone, can do the sa  [#permalink]

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13 Feb 2016, 08:01
Bunuel wrote:
Dan can do a job alone in 15 hours. Fred, working alone, can do the same job in just 10 hours. If Dan works alone for 9 hours and then stops, how many hours will it take Fred, working alone, to complete the job?

A. 4
B. 5
C. 6
D. 12
E. 12.5

Rate = work / time (for work in this problem use 1 to represent 1 job completed)

Dan's Rate = 1 / 15
Fred's Rate = 1/ 10

Work completed by Dan working for 9 hours by himself:
work = rate * time = ( 1/ 15) * 9 = 9 / 15

Amount of work for Fred to finish
1 - (9/15) = 6 / 15

Amount of time for Fred to finish the remaining work:
time = work / rate = (6/15) / (1/10) = 6/ 15* 10 = 4hrs
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Re: Dan can do a job alone in 15 hours. Fred, working alone, can do the sa  [#permalink]

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27 Feb 2016, 04:57
Can I do this way?

Dan rate is 15 hours
Fred rate is 10 hours

Implies, Dan is 1.5 or 3/2 times slower or vice versa.

Dan has already completed 9 hours of work and remaining is 6 hours. So, at the rate of 2/3rd, Fred can complete it in 2/3 * 6 =4.

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Re: Dan can do a job alone in 15 hours. Fred, working alone, can do the sa  [#permalink]

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15 May 2016, 14:25
1
Alternate Solution
Dan completes the full job in 15 hours working alone. He worked for 9 hours.
(9/15) *100 = 60% of the job is completed by Dan
Remaining 40% of the job is to be completed by Fred
As Fred takes 10 hours to complete the full job working alone
40 % of the remaining job can be completed by Fred in 4 hours

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Re: Dan can do a job alone in 15 hours. Fred, working alone, can do the sa  [#permalink]

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27 Nov 2019, 03:28
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Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Dan can do a job alone in 15 hours. Fred, working alone, can do the sa   [#permalink] 27 Nov 2019, 03:28
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