Bunuel wrote:
John works twice as fast as Peter, but John takes a half hour break after every one hour worked while Peter takes an hour break after every two hours worked. If John can complete the task in 5 hours working alone with no breaks, how long will it take both to complete the task if they start working together while maintaining their break habits?
A. 3 hours and 20 minutes
B. 4 hours and 30 minutes
C. 4 hours and 40 minutes
D. 4 hours and 45 minutes
E. 5 hours
The rate of John is 1/5 and the rate of Peter is 1/10.
Their combined rate, with no breaks is, 1/5 + 1/10 = 2/5 + 1/10 = 3/10.
For the first 3 hours of working together, we see that each would have taken a one-hour break and thus each worked only 2 hours. Thus, they finished 2 x 3/10 = 6/10 of the job.
During the next hour, hour 4, they both worked for the full hour; thus, they finished another 3/10 of the job and so far they finished 6/10 + 3/10 = 9/10 of the job.
During the following hour, hour 5, John worked only half an hour (since he took a half-hour break) while Peter worked the full hour; thu,s they would have completed another ½(1/5) + 1/10 = 2/10 of the job. However, by the end of hour 5, we see that they would have completed 9/10 + 2/10 = 11/10 or more than 1 entire job. Thus we need to push the time back.
So let’s only focus on the first 30 minutes of hour 5; John would not be working since he’s on his half-hour break, while Peter worked the entire 30 minutes. Thus, Peter would have completed another ½(1/10) = 1/20 of the job. By the end of the first 30 minutes of hour 5, we see that they would have completed 9/10 + 1/20 = 19/20 of the job.
We see that it takes more than 4 hour 30 minutes but less than 5 hours to complete this job. We also see that there are two answer choices that are between these two times. Let’s analyze choice C, 4 hours and 40 minutes, first. In other words, let’s see how much more work they complete in the extra 10 minutes.
In the extra 10 minutes, or ⅙ of an hour, they were both working; thus, they completed ⅙(1/5) + ⅙(1/10) = 1/30 + 1/60 = 3/60 = 1/20 of the job. Add this to the 19/20 of the job they completed in 4 hours 30 minutes, and we see that they would have completed exactly one entire job.
Answer: C
_________________
Jeffery Miller
Head of GMAT Instruction
GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions
35% (02:52) correct 
