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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # John works twice as fast as Peter, but John takes a half hour break af

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Math Expert V
Joined: 02 Sep 2009
Posts: 59083
John works twice as fast as Peter, but John takes a half hour break af  [#permalink]

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18 00:00

Difficulty:   95% (hard)

Question Stats: 36% (03:26) correct 64% (03:22) wrong based on 225 sessions

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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

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Marshall & McDonough Moderator D
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Location: India
Re: John works twice as fast as Peter, but John takes a half hour break af  [#permalink]

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2
2
Rate of John = 2*(Rate of Peter)

Rate of John = 1/5 = 2/10
Rate of Peter = 1/10

Combined rate = 3/10

In 3 hours, Peter and John work for 2 hrs each --> Work done = 6/10
They work together for the next 1 hour --> Work done = 3/10
Work remaining = 1 - 9/10 = 1/10

In the next one hour peter takes half an hour break and john works actively for the entire hour.
Work done by John in half an hour = 1/20
Work remaining = 2/20 - 1/20 = 1/20

Time taken to complete the remaining work = (3/10) * x = 1/20
x = 1/6 hrs = 10 mins

Total time taken = 3hrs + 1hr + 30 mins + 10 mins = 4 hr 40 mins

Senior PS Moderator V
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John works twice as fast as Peter, but John takes a half hour break af  [#permalink]

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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

Let us assume the total work to be 1000 units

Since John completes the work in 5 hours(without any breaks), he must be doing 200 units/hour

As John works twice as fast as Peter, the rate at which Peter does the work must be 100 units/hour

Rate at which they take breaks are as follows:
John takes a half an hour break for an hour of work
Peter takes an hour break for two hours of work.

John does 200 units in $$1\frac{1}{2}$$ hour, effectively doing 600 units in $$4\frac{1}{2}$$ hours.

Peter does 200 units in 3 hours. In the additional $$1\frac{1}{2}$$ hour of work, he would have completed 150 units of work.
Therefore, Peter does 350 units in $$4\frac{1}{2}$$ hours

In $$4\frac{1}{2}$$ hours John and Peter would have completed 950 units of work.
For the remaining 50 units, working at 300 units/hour, they would take an additional 10 minutes.

Therefore, the total time taken to complete the 1000 units of work is 4 hours and 40 minutes(Option C)
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Re: John works twice as fast as Peter, but John takes a half hour break af  [#permalink]

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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.

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Re: John works twice as fast as Peter, but John takes a half hour break af  [#permalink]

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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

Hi Bunuel , any suggestion on how to calculate this in a quicker way? Using some algebra or work rate formula?
I calculated the time it would took to do the job without any breaks which is 3 hours and 20 minutes , and then I tried to add the "break time" , but I got lost at some point.....I don't think is the right way to do it...
Intern  B
Joined: 27 Oct 2015
Posts: 5
Re: John works twice as fast as Peter, but John takes a half hour break af  [#permalink]

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2
2
Easiest method--
John can complete work in 5 hours (Given in the statement). Hence, we can derive that Peter can complete same work in 10 hours (John works twice as fast as Peter).
Now, It's provided that

""John takes a half hour break after every one hour worked." 5 hours job now will be completed in 7 hours by John(BE CAUTIOUS. It wont be 7.5 hours).....

"while Peter takes an hour break after every two hours worked." 10 hours job now will be completed in 14 hours by Peter(BE CAUTIOUS. It won't be 15 hours).....

To find new combined time-- 7*14/21 hours---->4 hours and 40 minutes
Intern  B
Joined: 10 Jul 2017
Posts: 9
Re: John works twice as fast as Peter, but John takes a half hour break af  [#permalink]

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J=2P
J takes 5hrs so P ll take 10hrs
Let total work be 10units(lcm of 5 n 10)
J-5 hrs so 2units/hr
P-10 hrs so 1unit/hr
1st hr-3units
2nd hr-2units
3rd hr-1unit
4th hr-3 units
In next 30min
J- 0 units(rest)
P- 0.5 units
So 10-9.5=0.5 units they have to do together without rest.

Without rest they take 10/3hrs for completing 10 units, so for 0.5 units they lol take (10/3)*(1/10)*(1/2)=(1/6)hr= 10 min

So total 4hrs 40min(C)

Sent from my CPH1609 using GMAT Club Forum mobile app
Intern  B
Joined: 10 Jul 2017
Posts: 9
Re: John works twice as fast as Peter, but John takes a half hour break af  [#permalink]

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Staphyk wrote:
Hello! Bunuel is there a much quicker way to solve question like this?

Sent from my iPhone using GMAT Club Forum

U can try hourly calculation,easiest method.
20043856 wrote:
Easiest method--
John can complete work in 5 hours (Given in the statement). Hence, we can derive that Peter can complete same work in 10 hours (John works twice as fast as Peter).
Now, It's provided that

""John takes a half hour break after every one hour worked." 5 hours job now will be completed in 7 hours by John(BE CAUTIOUS. It wont be 7.5 hours).....

"while Peter takes an hour break after every two hours worked." 10 hours job now will be completed in 14 hours by Peter(BE CAUTIOUS. It won't be 15 hours).....

To find new combined time-- 7*14/21 hours---->4 hours and 40 minutes

Sent from my CPH1609 using GMAT Club Forum mobile app
Intern  B
Joined: 20 Mar 2018
Posts: 1
John works twice as fast as Peter, but John takes a half hour break af  [#permalink]

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1
Rj = 1/5 = 2/10
Rp = 1/10

It is known that John takes a 30' brake every one hour of work, hence his productivity (Rate of work) decreases. By taking into consideration the breaks, John needs 5 working hours plus 4*30' breaks (no need to take a break when the job is done). Having said that:

Rj' = 1/7
Rp' = 1/14 (Following the same logic)

R=W/t => 2/14 + 1/14 = 1/t => t = 14/3 = 4h and 2/3

D
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Joined: 20 Mar 2018
Posts: 401
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Re: John works twice as fast as Peter, but John takes a half hour break af  [#permalink]

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gyanapinku wrote:
Staphyk wrote:
Hello! Bunuel is there a much quicker way to solve question like this?

Sent from my iPhone using GMAT Club Forum

U can try hourly calculation,easiest method.
20043856 wrote:
Easiest method--
John can complete work in 5 hours (Given in the statement). Hence, we can derive that Peter can complete same work in 10 hours (John works twice as fast as Peter).
Now, It's provided that

""John takes a half hour break after every one hour worked." 5 hours job now will be completed in 7 hours by John(BE CAUTIOUS. It wont be 7.5 hours).....

"while Peter takes an hour break after every two hours worked." 10 hours job now will be completed in 14 hours by Peter(BE CAUTIOUS. It won't be 15 hours).....

To find new combined time-- 7*14/21 hours---->4 hours and 40 minutes

Sent from my CPH1609 using GMAT Club Forum mobile app
please how did you get the 7hrs and 14hrs and why not 7.5hrs and 15hrs

Sent from my iPhone using GMAT Club Forum mobile app
Manager  B
Joined: 09 Oct 2015
Posts: 224
Re: John works twice as fast as Peter, but John takes a half hour break af  [#permalink]

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Bigshorty wrote:
Rj = 1/5 = 2/10
Rp = 1/10

It is known that John takes a 30' brake every one hour of work, hence his productivity (Rate of work) decreases. By taking into consideration the breaks, John needs 5 working hours plus 4*30' breaks (no need to take a break when the job is done). Having said that:

Rj' = 1/7
Rp' = 1/14 (Following the same logic)

R=W/t => 2/14 + 1/14 = 1/t => t = 14/3 = 4h and 2/3

D

is this a fool proof way of solving this type of question?
Bunuel chetan2u
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Re: John works twice as fast as Peter, but John takes a half hour break af  [#permalink]

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Staphyk wrote:
gyanapinku wrote:
Staphyk wrote:
Hello! Bunuel is there a much quicker way to solve question like this?

Sent from my iPhone using GMAT Club Forum

U can try hourly calculation,easiest method.
20043856 wrote:
Easiest method--
John can complete work in 5 hours (Given in the statement). Hence, we can derive that Peter can complete same work in 10 hours (John works twice as fast as Peter).
Now, It's provided that

""John takes a half hour break after every one hour worked." 5 hours job now will be completed in 7 hours by John(BE CAUTIOUS. It wont be 7.5 hours).....

"while Peter takes an hour break after every two hours worked." 10 hours job now will be completed in 14 hours by Peter(BE CAUTIOUS. It won't be 15 hours).....

To find new combined time-- 7*14/21 hours---->4 hours and 40 minutes

Sent from my CPH1609 using GMAT Club Forum
please how did you get the 7hrs and 14hrs and why not 7.5hrs and 15hrs

Sent from my iPhone using GMAT Club Forum

Because the last half hour (for John) and the last hour (for Peter) are break time when they already finished their work.

In case of John:
He works from 0h to 1h, takes break from 1h to 1.5h, then work from 1.5h to 2.5h, and so on.

0 -- work -- 1 -- break -- 1.5 -- work -- 2.5 -- break -- 3 -- work -- 4 -- break -- 4.5 -- work -- 5.5 -- break -- 6 -- work -- 7-- break -- 7.5

John complete the task in 7 hours. Break time from 7h to 7.5h should not be calculated in the time required for John to complete the task while maintaining his break habit.

The same logic is applied to the case of Peter.

Hope it helps.
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