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When A works alone, it takes 14hrs, and when A works with B together, [#permalink]
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09 Aug 2017, 04:29
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When A works alone, it takes 14hrs, and when A works with B together, it takes 10hrs. How many hours does it take B to work alone? A. 30hrs B. 33hrs C. 35hrs D. 37hrs E. 40hrs
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When A works alone, it takes 14hrs, and when A works with B together, [#permalink]
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09 Aug 2017, 04:39
MathRevolution wrote: When A works alone, it takes 14hrs, and when A works with B together, it takes 10hrs. How many hours does it take B to work alone? A. 30hrs B. 33hrs C. 35hrs D. 37hrs E. 40hrs Hi, Note: Consider total amount of work as LCM of no. of hours required by different persons. In this case, let's assume total amount of work = 70 units (LCM (14,10) = 70) Rate of A work = 70/14 = 5 units/hr Rate of A+B work = 70/10 = 7 units/hr Rate of B work = 7  5 = 2 units/hr The total amount of time required to complete the work by B = 70/2 = 35 hrs. Answer: (C) Thanks.
Last edited by ganand on 10 Aug 2017, 00:21, edited 1 time in total.



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Re: When A works alone, it takes 14hrs, and when A works with B together, [#permalink]
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09 Aug 2017, 05:20
Lets arrange the Information and assume that 1 unit of work needs to be done.
Work = Rate * Time A: 1 = * 14 B: 1 = * T A+B: 1 = * 10
Now we fill in what we can deduct
Work = Rate * Time A: 1 = 1/14 * 14 B: 1 = 1/T * T A+B: 1 = 1/10 * 10
What we need is T. If we add the rates of A and B we get the combined rate A+B.
(1/14) + (1/T) = (1/10) =>(T+14 / 14T) = (1/10) =>T+14 = (14T/10) =>10T + 140 = 14T =>140 = 4T =>T = 35
Answer C



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Re: When A works alone, it takes 14hrs, and when A works with B together, [#permalink]
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09 Aug 2017, 09:03
MathRevolution wrote: When A works alone, it takes 14hrs, and when A works with B together, it takes 10hrs. How many hours does it take B to work alone? A. 30hrs B. 33hrs C. 35hrs D. 37hrs E. 40hrs Let the total work be = 70 Efficiency of A = 5 Efficiency of A + B = 7 So, Efficiency of B = 2 So, Time taken by B to work alone is \(\frac{70}{2}\) = \(35\) hours.. Thus, answer must be (C)
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When A works alone, it takes 14hrs, and when A works with B together, [#permalink]
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09 Aug 2017, 09:10
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MathRevolution wrote: When A works alone, it takes 14hrs, and when A works with B together, it takes 10hrs. How many hours does it take B to work alone? A. 30hrs B. 33hrs C. 35hrs D. 37hrs E. 40hrs There are a few ways to solve these problems. If possible, I find adding rates the easiest. "It" is one job, or one unit of work. (Rate of A and B together)  (rate of A) = (rate of B) \(\frac{1}{10}\)  \(\frac{1}{14}\) =\(\frac{(14  10)}{140}\) = \(\frac{4}{140}\) = \(\frac{1}{35}\) > B's rate When work unit is one, flip the rate to get the time: 1/(1/35) = 35 Answer C
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Re: When A works alone, it takes 14hrs, and when A works with B together, [#permalink]
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09 Aug 2017, 19:39
Abhishek009 wrote: MathRevolution wrote: When A works alone, it takes 14hrs, and when A works with B together, it takes 10hrs. How many hours does it take B to work alone? A. 30hrs B. 33hrs C. 35hrs D. 37hrs E. 40hrs Let the total work be = 70 Efficiency of A = 5 Efficiency of A + B = 7 So, Efficiency of B = 2 So, Time taken by B to work alone is \(\frac{70}{2}\) = \(35\) hours.. Thus, answer must be (C)Hello, How do you assume A= 5? Thank you very much



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Re: When A works alone, it takes 14hrs, and when A works with B together, [#permalink]
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09 Aug 2017, 20:04
Hi pclawong, It is not so much as assumption in this case. Here, the total units of work is 70 units and since A (when working alone) does the work in 14 hours, A's efficieny is 70/14 = 5 units Similarly, Since both do the work in 10 hours, their combined efficiency is 7 units. This makes the efficiency of B(2 units), and the time it takes him to complete the work 35 hours(Option C) Hope that helps you!
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Re: When A works alone, it takes 14hrs, and when A works with B together, [#permalink]
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11 Aug 2017, 01:03
==> For work rate questions, you solve “together and alone” reciprocally. It takes A 14hrs alone, and if you set the hours it took B to work alone as B hrs, from \((\frac{1}{14})+(\frac{1}{B})=\frac{1}{10}\) and \(\frac{1}{B}=(\frac{1}{10})(\frac{1}{14})=\frac{1}{35}\), you get \(B=35\). The answer is C. Answer: C
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