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James can complete a job in 6 hours and Sarah can complete the same jo

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James can complete a job in 6 hours and Sarah can complete the same jo  [#permalink]

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08 Feb 2019, 12:44
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James can complete a job in 6 hours and Sarah can complete the same job in 4 $$\frac{1}{2}$$ hours. If James works on the job alone for a certain amount of time and Sarah works on the job alone for half as long as James, and it takes 1 hour for them to complete the remainder of the job together, how long did James work on the job alone?

A. 1 hour, 6 minutes
B. 1 hour, 10 minutes
C. 2 hours, 12 minutes
D. 2 hours, 20 minutes
E. 3 hours, 18 minutes

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Re: James can complete a job in 6 hours and Sarah can complete the same jo  [#permalink]

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08 Feb 2019, 18:51
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James can complete a job in 6 hours and Sarah can complete the same job in 4 $$\frac{1}{2}$$ hours. If James works on the job alone for a certain amount of time and Sarah works on the job alone for half as long as James, and it takes 1 hour for them to complete the remainder of the job together, how long did James work on the job alone?

A. 1 hour, 6 minutes
B. 1 hour, 10 minutes
C. 2 hours, 12 minutes
D. 2 hours, 20 minutes
E. 3 hours, 18 minutes

Let J work for 2x hours alone, so S works alone for x hours..
Both combined, can do 2/9+1/6=7/18 or work in 1 hour...
So 2x/6+2x/9+7/18=1.....(6x+4x)/18=11/18....x=1.1=1hr 6 minutes..
James works alone for 2x, so 2hrs 12 min

C
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Re: James can complete a job in 6 hours and Sarah can complete the same jo  [#permalink]

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09 Feb 2019, 00:10
1
James can complete a job in 6 hours and Sarah can complete the same job in 4 $$\frac{1}{2}$$ hours. If James works on the job alone for a certain amount of time and Sarah works on the job alone for half as long as James, and it takes 1 hour for them to complete the remainder of the job together, how long did James work on the job alone?

A. 1 hour, 6 minutes
B. 1 hour, 10 minutes
C. 2 hours, 12 minutes
D. 2 hours, 20 minutes
E. 3 hours, 18 minutes

Since James can complete the job in 6 hours and Sarah in 4.5 hours, lets total work
be 54 units. We choose 54 as it is a number that is compatible with both the times.

The rates at which James and Sarah do the work is 9 units and 12 units
respectively. In 1 hour, they will both complete 21(9 + 12) units of work.

Let the time on which James does the work alone be x hours.

James will do is 9x units or work and Sarah does $$12(\frac{x}{2})$$ or $$6x$$ units.

$$9x + 6x + 21 = 54$$ -> $$15x = 54 - 21 = 33$$ -> $$x = \frac{33}{15} = 2\frac{1}{5}$$ hours

Therefore, the total time that James works on the job alone is 2 hours, 12 minutes(Option C)
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Re: James can complete a job in 6 hours and Sarah can complete the same jo  [#permalink]

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09 Feb 2019, 00:12
1
James can complete a job in 6 hours and Sarah can complete the same job in 4 $$\frac{1}{2}$$ hours. If James works on the job alone for a certain amount of time and Sarah works on the job alone for half as long as James, and it takes 1 hour for them to complete the remainder of the job together, how long did James work on the job alone?

A. 1 hour, 6 minutes
B. 1 hour, 10 minutes
C. 2 hours, 12 minutes
D. 2 hours, 20 minutes
E. 3 hours, 18 minutes

rate of James= 1/6 and rate of Sarah = 2/9

let time of James = 2hrs and Sarah = 1 hour

work done by both James & Sarah ; 1/6+2/9 = 7/18 in 1 hr

so
total work done
2x/6+2x/9+7/18 = 1
x= 1.1 hrs or 1 hr 6 mins
James work is for 2 hours
so 2*1.1 = 2 hrs 12 mins
IMO C
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Re: James can complete a job in 6 hours and Sarah can complete the same jo  [#permalink]

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09 Feb 2019, 00:21
1
James can complete a job in 6 hours and Sarah can complete the same job in 4 $$\frac{1}{2}$$ hours. If James works on the job alone for a certain amount of time and Sarah works on the job alone for half as long as James, and it takes 1 hour for them to complete the remainder of the job together, how long did James work on the job alone?

A. 1 hour, 6 minutes
B. 1 hour, 10 minutes
C. 2 hours, 12 minutes
D. 2 hours, 20 minutes
E. 3 hours, 18 minutes

Lets take work as 36 units

James rate = 36/6 = 6 units/hr
Sarah rate = 8 units / hr

1 hour for them to complete the remainder of the job together, means remaining work = 36-14 = 22 units

W = rate *time

let time taken by James to complete the work be x
If James works on the job alone for a certain amount of time and Sarah works on the job alone for half as long as James

6x + 4x = 22
x = 22/10 = 11/5

how long did James work on the job alone = 2 hours, 12 minutes
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Re: James can complete a job in 6 hours and Sarah can complete the same jo   [#permalink] 09 Feb 2019, 00:21
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