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# John takes 15 hours to complete a certain job, while Bill takes only 6

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John takes 15 hours to complete a certain job, while Bill takes only 6 [#permalink]

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19 Jun 2015, 01:39
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John takes 15 hours to complete a certain job, while Bill takes only 6 hours to complete the same job. If Steve is faster than John but slower than Bill at completing the same job, then which of the following could be the time it takes the three men together, working at their constant, individual rates, to complete the job?

A. 2 hours, 30 minutes
B. 2 hours, 45 minutes
C. 3 hours, 20 minutes
D. 3 hours, 45 minutes
E. 4 hours, 10 minutes

Kudos for a correct solution.
[Reveal] Spoiler: OA

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Re: John takes 15 hours to complete a certain job, while Bill takes only 6 [#permalink]

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19 Jun 2015, 03:27
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Its Option B here.

John can complete the work in 15 hours so the amount of work completed in hour= 1/15

Bill can complete the work in 6 hours, so the amount of work complete in one hour= 1/6

1/15+ 1/6 = 7/30.

Option 1: 7/30+ 1/ X = 2/5 => X= 6 hours.

Option 2: 7/30 + 1/X= 4/11 (x=Around 7. 5 ish...)

Option 3: 7/30 + 1/x = 3/10 (X is 15)

OPTION 4 and 5 will be definitely greater than 15. Hence Option B correct.

(As bills work will be between 6 and 15)

Bunuel wrote:
John takes 15 hours to complete a certain job, while Bill takes only 6 hours to complete the same job. If Steve is faster than John but slower than Bill at completing the same job, then which of the following could be the time it takes the three men together, working at their constant, individual rates, to complete the job?

A. 2 hours, 30 minutes
B. 2 hours, 45 minutes
C. 3 hours, 20 minutes
D. 3 hours, 45 minutes
E. 4 hours, 10 minutes

Kudos for a correct solution.

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Re: John takes 15 hours to complete a certain job, while Bill takes only 6 [#permalink]

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19 Jun 2015, 03:32
Bunuel wrote:
John takes 15 hours to complete a certain job, while Bill takes only 6 hours to complete the same job. If Steve is faster than John but slower than Bill at completing the same job, then which of the following could be the time it takes the three men together, working at their constant, individual rates, to complete the job?

A. 2 hours, 30 minutes
B. 2 hours, 45 minutes
C. 3 hours, 20 minutes
D. 3 hours, 45 minutes
E. 4 hours, 10 minutes

Kudos for a correct solution.

Set up a rate/time/work table and plug in 30 as for the "work":

John 2 15 30
Bill 5 6 30
Steve >2, <5 ?

Compound R X 30

Plug in the answer choices in the function of the compound rate. If you plug in A which is 2.5 hours, Steves Rate would be 5 which is not smaller than Bills rate. Answer Choice B fits, making Steve's Rate 3.9.

AC B.
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Re: John takes 15 hours to complete a certain job, while Bill takes only 6 [#permalink]

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19 Jun 2015, 08:23
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Bunuel wrote:
John takes 15 hours to complete a certain job, while Bill takes only 6 hours to complete the same job. If Steve is faster than John but slower than Bill at completing the same job, then which of the following could be the time it takes the three men together, working at their constant, individual rates, to complete the job?

A. 2 hours, 30 minutes
B. 2 hours, 45 minutes
C. 3 hours, 20 minutes
D. 3 hours, 45 minutes
E. 4 hours, 10 minutes

Kudos for a correct solution.

we can find two extreme ends, which are just out of the range
1) lower end... j=15h, b=6h and j=15h
all three will take$$\frac{1}{( 1/15+1/15+1/6)}$$= 2h 30 min
2) higher end j=15h, b=6h and j=6h
all three will take$$\frac{1}{( 1/15+1/6+1/6)}$$= 3h 20 min..

only B is within this range
ans B
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Re: John takes 15 hours to complete a certain job, while Bill takes only 6 [#permalink]

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20 Jun 2015, 02:51
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Bunuel wrote:
John takes 15 hours to complete a certain job, while Bill takes only 6 hours to complete the same job. If Steve is faster than John but slower than Bill at completing the same job, then which of the following could be the time it takes the three men together, working at their constant, individual rates, to complete the job?

A. 2 hours, 30 minutes
B. 2 hours, 45 minutes
C. 3 hours, 20 minutes
D. 3 hours, 45 minutes
E. 4 hours, 10 minutes

Kudos for a correct solution.

Hello,
We can answer this by obtaining values for the extremes as per the stated conditions. Correct answer will fall in between the extremes. It is told that Steve is faster than John i.e he takes less than 15 hours and greater than Bill i.e. he takes more than 6 hours.

Step 1 : Let's calculate one extreme by assuming Steve took the same amount as John to complete the work. The total time taken by three then will be 1/15+1/15+1/6 ( rates respective for John, Steve and Bill) which equals 3 hours 20 mins. (Applied RT=W)

Step 2 : Let's calculate other extreme by assuming Steve took the same amount as Bill to complete the work. The total time taken by three then will be 1/15+1/6+1/6 (rates respective for John, Steve and Bill) which equals 2 hours 30 mins. (Applied RT=W)

The correct answer shall fall in between these two values and looking at answer choices we see that only option B is the value that does so.

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Re: John takes 15 hours to complete a certain job, while Bill takes only 6 [#permalink]

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20 Jun 2015, 06:24
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Bunuel wrote:
John takes 15 hours to complete a certain job, while Bill takes only 6 hours to complete the same job. If Steve is faster than John but slower than Bill at completing the same job, then which of the following could be the time it takes the three men together, working at their constant, individual rates, to complete the job?

A. 2 hours, 30 minutes
B. 2 hours, 45 minutes
C. 3 hours, 20 minutes
D. 3 hours, 45 minutes
E. 4 hours, 10 minutes

Kudos for a correct solution.

I assumed S = 1/10.. 1/15 + 1/6 + 1/10 = 3/9 j/h ... = 9/3h/j = 3h

Question is..which could be the time ? Hence, why is C incorrect ?

Last edited by LaxAvenger on 20 Jun 2015, 06:38, edited 1 time in total.

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Re: John takes 15 hours to complete a certain job, while Bill takes only 6 [#permalink]

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20 Jun 2015, 06:35
It is given in the question statement that Steve takes less time then John. They take exactly 3hrs20mins if Steve takes exactly the same amount of time as John, but we know that it is not the case. So the total time taken should be less than 3hrs 20 mins and more than 2hrs 30mins as these are the two extreme values obtained as per the statement. Hope I am clear ?

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Re: John takes 15 hours to complete a certain job, while Bill takes only 6 [#permalink]

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20 Jun 2015, 06:42
LaxAvenger wrote:
Bunuel wrote:
John takes 15 hours to complete a certain job, while Bill takes only 6 hours to complete the same job. If Steve is faster than John but slower than Bill at completing the same job, then which of the following could be the time it takes the three men together, working at their constant, individual rates, to complete the job?

A. 2 hours, 30 minutes
B. 2 hours, 45 minutes
C. 3 hours, 20 minutes
D. 3 hours, 45 minutes
E. 4 hours, 10 minutes

Kudos for a correct solution.

I assumed S = 1/10.. 1/15 + 1/6 + 1/10 = 3/9 j/h ... = 9/3h/j = 3h

Question is..which could be the time ? Hence, why is C incorrect ?

hi,
you have assumed 1/10 correctly but solved it wrongly..
$$\frac{1}{10}+\frac{1}{15}+\frac{1}{6}=\frac{(3+2+5)}{30}=\frac{10}{30}=\frac{1}{3}$$
so ans is 3 hrs and not 3 hrs 20 min...
if 3 hrs was a choice it would have been correct
hope it is clear now
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Re: John takes 15 hours to complete a certain job, while Bill takes only 6 [#permalink]

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20 Jun 2015, 06:46
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we can find two extreme ends, which are just out of the range

1) lower end... j=15h, b=6h and j=15h
all three will take1(1/15+1/15+1/6)= 2h 30 min
2) higher end j=15h, b=6h and j=6h
all three will take1(1/15+1/6+1/6)= 3h 20 min..

only B is within this range
ans B

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Re: John takes 15 hours to complete a certain job, while Bill takes only 6 [#permalink]

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20 Jun 2015, 06:47
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chetan2u wrote:
LaxAvenger wrote:
Bunuel wrote:
John takes 15 hours to complete a certain job, while Bill takes only 6 hours to complete the same job. If Steve is faster than John but slower than Bill at completing the same job, then which of the following could be the time it takes the three men together, working at their constant, individual rates, to complete the job?

A. 2 hours, 30 minutes
B. 2 hours, 45 minutes
C. 3 hours, 20 minutes
D. 3 hours, 45 minutes
E. 4 hours, 10 minutes

Kudos for a correct solution.

I assumed S = 1/10.. 1/15 + 1/6 + 1/10 = 3/9 j/h ... = 9/3h/j = 3h

Question is..which could be the time ? Hence, why is C incorrect ?

hi,
you have assumed 1/10 correctly but solved it wrongly..
$$\frac{1}{10}+\frac{1}{15}+\frac{1}{6}=\frac{(3+2+5)}{30}=\frac{10}{30}=\frac{1}{3}$$
so ans is 3 hrs and not 3 hrs 20 min...
if 3 hrs was a choice it would have been correct
hope it is clear now

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Re: John takes 15 hours to complete a certain job, while Bill takes only 6 [#permalink]

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22 Jun 2015, 06:37
Expert's post
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BOOKMARKED
Bunuel wrote:
John takes 15 hours to complete a certain job, while Bill takes only 6 hours to complete the same job. If Steve is faster than John but slower than Bill at completing the same job, then which of the following could be the time it takes the three men together, working at their constant, individual rates, to complete the job?

A. 2 hours, 30 minutes
B. 2 hours, 45 minutes
C. 3 hours, 20 minutes
D. 3 hours, 45 minutes
E. 4 hours, 10 minutes

Kudos for a correct solution.

VERITAS PREP GMAT OFFICIAL SOLUTION:

In this Work/Rate problem, it's important to recognize first that rates are additive, so the combined rate of the three men will be:

1/15 + 1/6 + 1/S, which is John's rate plus Bill's rate plus Steve's rate.

For Steve's rate, we're told that it's between John's and Bill's, so you can set up the inequality:

1/15 < 1/S < 1/6

So to set the limits for how long it can take the three men at the low end and at the high end, you can set 1/S equal to 1/15 and to 1/6, and then you know that the actual time has to be between those. The fastest it could go, then is just a hair longer than it would be if the rates were:

1/6 + 1/6 + 1/15, which simplifies to 1/3 + 1/15, which then becomes 5/15 + 1/15 = 6/15 = 2/5. And since 2/5 is a rate (equal to output over time), you can phrase this as "to do two jobs takes 5 hours, so to do one job takes 2.5. So the job has to take longer than 2.5 hours, eliminating choice A.

Here's where an astute test-taker can stop. You know that the task has to take longer than 2:30 and shorter than "whatever you'd calculate next". But since the next calculation will set the higher limit AND since you can't have two correct answers, there's no way the upper limit would include C, D, or E and somehow exclude B. So the answer has to be B.

But to finish that math, you can solve for the time it takes if Steve's time is just a hair faster than John's. That would be:

1/15 + 1/15 + 1/6, which simplifies to 2/15 + 1/6. That's 4/30 + 5/30 = 9/30, which simplifies to 3/10. Again, that's "it would take 10 hours to do 3 jobs" so it will take 3 hour and 20 minutes to do one job. Since Steve has to be just a bit faster than John's, it has to take a little less than 3:20, so you can set the upper limit just shy of choice C, guaranteeing that the answer is B.
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Re: John takes 15 hours to complete a certain job, while Bill takes only 6 [#permalink]

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30 Oct 2015, 17:29
damn..I chose a very long way to solve it..thus..spending a lot of time
since S works faster than J, but slower than B, we can take extremities
S = 14
S = 7

by solving this, we see that the time is between 2h30+m and 3h16m
the only answer choice that falls between this interval is B.

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Re: John takes 15 hours to complete a certain job, while Bill takes only 6 [#permalink]

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18 Mar 2016, 22:04
Bunuel wrote:
John takes 15 hours to complete a certain job, while Bill takes only 6 hours to complete the same job. If Steve is faster than John but slower than Bill at completing the same job, then which of the following could be the time it takes the three men together, working at their constant, individual rates, to complete the job?

A. 2 hours, 30 minutes
B. 2 hours, 45 minutes
C. 3 hours, 20 minutes
D. 3 hours, 45 minutes
E. 4 hours, 10 minutes

Kudos for a correct solution.

John and Bill complete the work in 90/21 hours; if Steve joins them, the time taken to complete the job will be less than this time.
Steve's time taken is between 15 hours and 6 hours.
Find the limiting value for 90/21 and 15 and 90/21 and 6; that gives 3 hours 20 m and 2 hours and 30 min
That implies the answer has to be between these limits.

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John takes 15 hours to complete a certain job, while Bill takes only 6 [#permalink]

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17 Jun 2017, 22:00
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Assume the units of work to be 90

Since John takes 15 hours to finish the work, the rate of John's work is 6 units/hour
Similarly, Bill take 6 hours to finish the work, the rate of Bill's work is 15 units/hour

Since it has been given that the rate of Steve is greater than John and lesser than Bill,
the range of Steve's rate is between 6 units/hour and 15 units/hour
Hence the range of the time take to complete the work is between
$$\frac{90}{(6+6+15)}$$ = 3.33 hours(3 hour, 20 mins) and $$\frac{90}{(6+15+15)}$$ = 2.5 hours(2 hour, 30 mins)

The only value within this range is 2 hour, 45 mins(Option B)
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Re: John takes 15 hours to complete a certain job, while Bill takes only 6 [#permalink]

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02 Jul 2017, 06:36
hi, could you plz explain how 2/5, 4/11 and 3/10 came?

shriramvelamuri wrote:
Its Option B here.

John can complete the work in 15 hours so the amount of work completed in hour= 1/15

Bill can complete the work in 6 hours, so the amount of work complete in one hour= 1/6

1/15+ 1/6 = 7/30.

Option 1: 7/30+ 1/ X = 2/5 => X= 6 hours.

Option 2: 7/30 + 1/X= 4/11 (x=Around 7. 5 ish...)

Option 3: 7/30 + 1/x = 3/10 (X is 15)

OPTION 4 and 5 will be definitely greater than 15. Hence Option B correct.

(As bills work will be between 6 and 15)

Bunuel wrote:
John takes 15 hours to complete a certain job, while Bill takes only 6 hours to complete the same job. If Steve is faster than John but slower than Bill at completing the same job, then which of the following could be the time it takes the three men together, working at their constant, individual rates, to complete the job?

A. 2 hours, 30 minutes
B. 2 hours, 45 minutes
C. 3 hours, 20 minutes
D. 3 hours, 45 minutes
E. 4 hours, 10 minutes

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Re: John takes 15 hours to complete a certain job, while Bill takes only 6 [#permalink]

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06 Sep 2017, 22:37
Let the total work to be done is 30
Rate of John and Bill is 2 and 5 respectively.
Now Rate of Steve is >2 and <5
So if rate is 2
Together they do 2+5+2 = 9 work / hour
So to complete 30 work they will take $$\frac{30}{9}$$ = 3 hrs 20 mins
If rate of work is 5
Together they do 2+5+5=12 work / hour
So to complete 30 work they will take $$\frac{30}{12}$$ = 2 hrs 30 mins
Thus answer should be between 2 hrs 30 mins and 3 hrs 20 mins
Only option is Option B
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Re: John takes 15 hours to complete a certain job, while Bill takes only 6 [#permalink]

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18 Sep 2017, 12:36
The idea is to find two extremes as implied in the question stem. What if Steve's rate was equal to John. In that case, the time taken would be:
(1/15 + 1/15 + 1/6) x t = w.
On solving, we get t = 3 hours 20mins.

Similarly, what if Steve's rate was equal to Bill. In that case, the time taken would be:
(1/15 + 1/6 + 1/6) x t = w.
On solving, we get t = 2 hours 30mins.

The only option in the middle of this range is Answer choice B. Hence the answer.
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Re: John takes 15 hours to complete a certain job, while Bill takes only 6   [#permalink] 18 Sep 2017, 12:36
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