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

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Senior RC Moderator
Joined: 02 Nov 2016
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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, 13:44
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65% (hard)

Question Stats:

56% (03:00) correct 44% (03:31) wrong based on 41 sessions

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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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Posts: 7957
Re: James can complete a job in 6 hours and Sarah can complete the same jo  [#permalink]

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08 Feb 2019, 19:51
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

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, 01:10
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, 01:12
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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Joined: 09 Mar 2018
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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, 01:21
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]

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15 Mar 2019, 13:25
Making a rates table:

1) Set work to be LCM of 6 and 4.5... 18
2) Find rate of James and Sarah

______r__t______W
James 3 * 6 hr = 18
Sarah 4 * 4.5 hr = 18

Next part:
______r__t_____W
James 3 * t hr =
Sarah 4 * 0.5t hr =
Ja+Sa 7 * 1 hr = 7

From this we can make the equation 3t+2t = 11 (James' work + Sarah's work = 11 remaining out of 18)
So, t = 11/5 OR 2 and 1/5 hours... 1/5 of an hour is 12 minutes so the answer is C.
Or just set up the ratio 11 hrs/5 * 60 min/1 hr = 132 minutes or 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]

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15 Jul 2019, 07:32
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

James does = 1/6 units in 1 hour
Sarah does = 9/2 units in 1 hour
Together they do = 1/6 + 2/9 = 7/18 units in 1 hour
Before this 1 hour of working together , they were working alone...
They did the rest = 1 - 7/18 = 11/18 units working alone...
Lets say , James worked for x hours during that time ...
And Sarah worked for x/2 hours...
So
x/6 + x/9 = 11/18

x= 11/5 hours...

Please give me Kudos if you liked my explanation.
Re: James can complete a job in 6 hours and Sarah can complete the same jo   [#permalink] 15 Jul 2019, 07:32
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