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

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Bunuel
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James can complete a job in 6 hours and Sarah can complete the same jo [#permalink] New post   07 Sep 2021, 03:30
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68% (02:49) correct 32% (03:11) 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 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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C
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yashikaaggarwal
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Re: James can complete a job in 6 hours and Sarah can complete the same jo [#permalink] New post   15 Sep 2021, 10:14
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LCM of 6 & 4.5 = 18
Total work = 18
Therefore,
James does 3 work in an hour.
Sarah does 4 work in an hour.

They work together for 1 hour to complete remaining work.
So, remaining work is ought to be 3+4 = 7
The first part of work done by both James and Sarah separately = 11
Let say
James do 3 work in 1 hour.
Sarah does 2 work in 1/2 HOUR.

They do 5 work in 1.5 hour
They will do 11 work in = X hours
X = 11*1.5/5
X = 3.3

James took 2/3 of total time.
3.3*2/3 = 2.2 hours.

2.2 hours = 2.2*60 = 132 minutes.
That's 2 hours and 12 minutes.

Answer is C

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Re: James can complete a job in 6 hours and Sarah can complete the same jo [#permalink] New post   25 Jan 2023, 11:46
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Bunuel wrote:
James can complete a job in 6 hours and Sarah can complete the same job in 4 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


The rate of James is 1/6 and the rate of Sarah is 1/4.5 = 10/45 = 2/9.

We can let the time James works = t and the time Sarah works = t/2. Thus, we can create the equation, which represents James working to t hours and 1 hour and Sarah working for t/2 and 1 hour:

1/6 + 2/9 + t/6 + (2/9 * t/2) = 1

1/6 + 2/9 + t/6 + t/9 = 1

Multiplying by 18, we have:

3 + 4 + 3t + 2t = 18

5t = 11

t = 11/5 = 2 1/5 hours = 2 hours and 12 minutes.

Answer: C
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Re: James can complete a job in 6 hours and Sarah can complete the same jo [#permalink] New post   25 Jan 2023, 13:16
Bunuel wrote:
James can complete a job in 6 hours and Sarah can complete the same job in 4 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



work done by james in one hour = 1/6

work done by sarah in one hour = 1/(9/2) --> 2/9

1 - [(1/6)*a - (2/9)*(a/2)] = [(1/6)+(2/9)]

1 = Total work
a = hours worked by A alone
a/2 = hours worked by B alone
[(1/6)+(2/9)] = remaining work done in 1 hour

a = 11/5 hrs --> 2.2 hours --> 2 hours + 0.2*60 minutes ---> 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]
25 Jan 2023, 13:16
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