GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 15 Aug 2018, 13:55

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# John works twice as fast as Peter, but John takes a half hour break af

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Manager
Joined: 02 Jun 2015
Posts: 192
Location: Ghana
John works twice as fast as Peter, but John takes a half hour break af  [#permalink]

### Show Tags

31 May 2017, 07:46
1
5
00:00

Difficulty:

85% (hard)

Question Stats:

57% (03:03) correct 43% (03:09) wrong based on 65 sessions

### HideShow timer Statistics

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

_________________

Kindly press kudos if you find my post helpful

Senior CR Moderator
Status: Long way to go!
Joined: 10 Oct 2016
Posts: 1394
Location: Viet Nam
John works twice as fast as Peter, but John takes a half hour break af  [#permalink]

### Show Tags

31 May 2017, 09:18
1
duahsolo 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

If $$x$$ is the performance each hour of Peter then $$2x$$ is the performance each hour of John.

John takes a half hour break after every one hour worked. This mean John took $$2x$$ work for every one and a half hour, or John took $$4x$$ work for every 3 hours.

Peter takes an hour break after every two hours worked. This mean Peter took $$2x$$ work for every 3 hours.

Hence, John and Peter took $$6x$$ work for every 3 hours.

Without break, John can complete the task in 5 hours. This means $$2x=\frac{1}{5} \implies x=\frac{1}{10}$$. This means John could complete $$\frac{1}{5}$$ of the task each hour and Peter could complete $$\frac{1}{10}$$ of the task each hour

Hence, John and Peter took $$\frac{6}{10}$$ of the work for every 3 hours.

In the first 3 hours, they completed $$\frac{6}{10}$$ of the task.
In the next hour, the 4th hour, they completed $$\frac{6}{10}+\frac{1}{5}+\frac{1}{10}=\frac{9}{10}$$ of the task. The remaining of the task is $$\frac{1}{10}$$

After that, John took a break after working for a hour, left Peter worked alone.

In the next half hour, the 4.5th hour, they completed $$\frac{9}{10} +\frac{1}{2} \times \frac{1}{10}=\frac{19}{20}$$. The reamining of the task is $$\frac{1}{20}$$.

After that, John went back to work. The performance of them now is $$\frac{1}{5} +\frac{1}{10}=\frac{3}{10}$$.

The remaining time they needed to completed the task is: $$\frac{1}{20} : \frac{3}{10}=\frac{10}{60}$$ hour or 10 minutes < 0.5 hour.

Hence, the total time they needed to completed the task is 4 hours 40 minutes. The answer is C.

Here is the image illustrates the process
Attachment:

Capture.PNG [ 8.04 KiB | Viewed 782 times ]

_________________
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 3161
Location: United States (CA)
Re: John works twice as fast as Peter, but John takes a half hour break af  [#permalink]

### Show Tags

10 Aug 2018, 18:40
duahsolo 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 = 2/10 + 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; thus, 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.

_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Re: John works twice as fast as Peter, but John takes a half hour break af &nbs [#permalink] 10 Aug 2018, 18:40
Display posts from previous: Sort by

# John works twice as fast as Peter, but John takes a half hour break af

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

# Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.