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Linda takes 4 hours to do a job, whereas Bob takes 6 hours to do the

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Linda takes 4 hours to do a job, whereas Bob takes 6 hours to do the  [#permalink]

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New post 25 Jul 2019, 23:42
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Linda takes 4 hours to do a job, whereas Bob takes 6 hours to do the same job. They worked together at their respective rates but Bob took two breaks of equal duration during the time. Despite that, the two of them were able to complete the job in 2 hours 30 minutes. What is the duration of each break that Bob took. ?

(A) 60 seconds
(B) 90 seconds
(C) 450 seconds
(D) 240 seconds
(E) 270 seconds

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Linda takes 4 hours to do a job, whereas Bob takes 6 hours to do the  [#permalink]

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New post 26 Jul 2019, 03:54
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Solution


Given:
    • Linda takes 4 hours to do a job
    • Bob takes 6 hours to do the same job.
    • They worked together at their respective rates but Bob took two breaks of equal duration during the time. Despite that, the two of them were able to complete the job in 2 hours 30 minutes

To find:
    • The duration of each break that Bob took

Approach and Working Out:
Let the total break time be “b” hours
    • So, for “b” hours out of 2 hours 30 minutes, Linda worked alone, and for the rest both worked together

Thus,
    • \((2.5 – b) * (\frac{1}{4} + \frac{1}{6}) + b * \frac{1}{4} = 1\)
    • \(\frac{12.5}{12} – \frac{b}{6} = 1\)
    • \(\frac{b}{6} = \frac{0.5}{12}\)
    • b = 0.25 hours = 15 minutes = 900 seconds

But 900 seconds is the total break time
    • Therefore, each break is of 450 seconds

Hence, the correct answer is Option C.

Answer: C

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Re: Linda takes 4 hours to do a job, whereas Bob takes 6 hours to do the  [#permalink]

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New post 26 Jul 2019, 00:17
If they both work together, it takes 2 hours and 24 minutes to finish the job.
(1/4+1/6)×X= 1
==》 X= 24/10=2.4= 2 hours and 24 minutes.
But they finished at 2h and 30m.
So, the break time has been 6 minutes or 240 seconds.
Option (D)

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Re: Linda takes 4 hours to do a job, whereas Bob takes 6 hours to do the  [#permalink]

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New post 26 Jul 2019, 03:57
Mohammadmo wrote:
If they both work together, it takes 2 hours and 24 minutes to finish the job.
(1/4+1/6)×X= 1
==》 X= 24/10=2.4= 2 hours and 24 minutes.
But they finished at 2h and 30m.
So, the break time has been 6 minutes or 240 seconds.
Option (D)

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Hi Mohammadmo,

There is a mistake in your approach. You have assumed that Linda also didn't work during the break time, but that is not the situation in this question.

We have posted our solution, please refer to it.

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Re: Linda takes 4 hours to do a job, whereas Bob takes 6 hours to do the  [#permalink]

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New post 26 Jul 2019, 07:07
Bunuel wrote:
Linda takes 4 hours to do a job, whereas Bob takes 6 hours to do the same job. They worked together at their respective rates but Bob took two breaks of equal duration during the time. Despite that, the two of them were able to complete the job in 2 hours 30 minutes. What is the duration of each break that Bob took. ?

(A) 60 seconds
(B) 90 seconds
(C) 450 seconds
(D) 240 seconds
(E) 270 seconds


Rate of Linda ; 1/4 and rate of Bob ; 1/6
let total work done = 1
and break of bob = x
given total time of work ; 2 hrs 30 mins or say 2 .5 hrs
since w=r*t
we can say
(2.5-b)*(10/24)+b*1/4 = 1
solve for b = 900 sec
each break = 900/2 ; 450 sec
IMO C
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Re: Linda takes 4 hours to do a job, whereas Bob takes 6 hours to do the  [#permalink]

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New post 26 Jul 2019, 08:01
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Bunuel wrote:
Linda takes 4 hours to do a job, whereas Bob takes 6 hours to do the same job. They worked together at their respective rates but Bob took two breaks of equal duration during the time. Despite that, the two of them were able to complete the job in 2 hours 30 minutes. What is the duration of each break that Bob took. ?

(A) 60 seconds
(B) 90 seconds
(C) 450 seconds
(D) 240 seconds
(E) 270 seconds


My Approach.
Assume work to be 24 Units (Because LCM)
Linda does 6 units and Bob does 4 units each hour to achieve 24 units of work.
If they are working together, Linda does 15 units of work in 2.5 hours and Bob should have done 10 units of work. (should because we know he took a break).
So basically he did one unit of work less of his own capacity for which he takes (15 minutes). and since that is 2 breaks of equal time, the break time is 7.5 minutes each.

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Re: Linda takes 4 hours to do a job, whereas Bob takes 6 hours to do the  [#permalink]

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New post 05 Aug 2019, 01:47
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Let me give you guys a simpler way to solve it.

Linda's rate= 1/4
Bob's rate= 1/6

Its only bob who took break, not linda and they both completed the work in 2.5 hrs

Work done by linda= 2.5 * 1/4 = 25/40

Work to be done by bob= 15/40

Time * 1/6 = 15/40
Time taken by bob to complete his share= 9/4 hrs (2 hrs 15 mins)

Hence, duration of two breaks is 15 mins.
Duration of 1 break in seconds= 15*1/2*60= 450 seconds.

IMO C

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Re: Linda takes 4 hours to do a job, whereas Bob takes 6 hours to do the   [#permalink] 05 Aug 2019, 01:47
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