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

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Bunuel
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Dan can do a job alone in 15 hours. Fred, working alone, can do the sa [#permalink] New post  07 Feb 2016, 10:11
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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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rhine29388
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Re: Dan can do a job alone in 15 hours. Fred, working alone, can do the sa [#permalink] New post  15 May 2016, 14:25
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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
correct answer - A

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

Answer A
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Tmoni26
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Re: Dan can do a job alone in 15 hours. Fred, working alone, can do the sa [#permalink] New post  12 Feb 2016, 10:15
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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
Answer Choice A
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sq01
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Re: Dan can do a job alone in 15 hours. Fred, working alone, can do the sa [#permalink] New post  13 Feb 2016, 08:01
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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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Thisisnatesh
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Re: Dan can do a job alone in 15 hours. Fred, working alone, can do the sa [#permalink] New post  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.

Thanks in advance.
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jayshaha
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Re: Dan can do a job alone in 15 hours. Fred, working alone, can do the sa [#permalink] New post  05 Aug 2020, 23:43
dan work 1/15
work completed 1/15*9=9/15
remaining work 6/15
fred work 1/10
6/15*10=4 days
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Re: Dan can do a job alone in 15 hours. Fred, working alone, can do the sa [#permalink]
05 Aug 2020, 23:43
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