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Joan can do an entire job in 12 hours. Ken can do an entire job in 6

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Bunuel
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Joan can do an entire job in 12 hours. Ken can do an entire job in 6 [#permalink] New post   05 May 2019, 23:35
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82% (01:28) correct 18% (01:46) wrong based on 137 sessions
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Joan can do an entire job in 12 hours. Ken can do an entire job in 6 hours. If Joan and Ken work together for 3 hours, how many hours will it take Ken to finish the rest of the job by himself?

A. 1
B. 1 1/2
C. 4 1/2
D. 6
E. 9
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B
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Re: Joan can do an entire job in 12 hours. Ken can do an entire job in 6 [#permalink] New post   05 May 2019, 23:54
Working together they finish 9/12 of the job
3/12 of the job remains.
Ken can finish it in 3/12÷1/6= 3/2
IMO B

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LevanKhukhunashvili
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Re: Joan can do an entire job in 12 hours. Ken can do an entire job in 6 [#permalink] New post   05 May 2019, 23:58
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LCM Method

Let assume that the whole job consists of 12 units
Joan -- \(\frac{12}{12}\)=1 \(\frac{unit}{hour}\)
ken -- \(\frac{12}{6}\)=2 \(\frac{unit}{hour}\)

together they can do 3 \(\frac{unit}{hour}\)
After working 3 hours together they have done 9 units, 3 units are left
Ken can do 3 units in \(\frac{3}{2}\)=1.5 hours

Another method
\(\frac{1}{12}\)+\(\frac{1}{6}\)=\(\frac{1}{4}\)
In 3 hours they have done \(\frac{3}{4}\) of the job, left \(\frac{1}{4}\)
Ken can do \(\frac{1}{4}\) of the job in \(\frac{6}{4}\)=1.5 hours

IMO
Ans: B
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Re: Joan can do an entire job in 12 hours. Ken can do an entire job in 6 [#permalink] New post   06 May 2019, 03:14
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Bunuel wrote:
Joan can do an entire job in 12 hours. Ken can do an entire job in 6 hours. If Joan and Ken work together for 3 hours, how many hours will it take Ken to finish the rest of the job by himself?

A. 1
B. 1 1/2
C. 4 1/2
D. 6
E. 9


rate of j = 1/12
rate of k=1/6
together work done
3x=4
x=4/3
work left ;1/4
so K will take time ; 1/4 * 6 = 3/2 IMO B ;
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Re: Joan can do an entire job in 12 hours. Ken can do an entire job in 6 [#permalink]
06 May 2019, 03:14
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