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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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.

Regards,
e-GMAT
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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.

Kudos if you feel like
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I also use LCM method to solve problem , but i am stuck after finding bob 10 unit of work.
Not able to understand this from your solution, Can you please make it more clear, how you came to 15 : (divide by 2 is clear)
" 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. "