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# Andy takes sqrt(x) hours to till x acres of land whereas

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Andy takes sqrt(x) hours to till x acres of land whereas [#permalink]

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24 Feb 2016, 15:22
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Andy takes $$\sqrt{x}$$ hours to till $$x$$ acres of land while Bill takes 10 minutes to till each acre of land. If they work together, approximately how many hours will they take to till 72 acres of land?

A. 2.5
B. 3.5
C. 6
D. 8.5
E. 12
[Reveal] Spoiler: OA

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Re: Andy takes sqrt(x) hours to till x acres of land whereas [#permalink]

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24 Feb 2016, 20:50
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TeamGMATIFY wrote:
Andy takes $$\sqrt{x}$$ hours to till $$x$$ acres of land while Bill takes 10 minutes to till each acre of land. If they work together, approximately how many hours will they take to till 72 acres of land?

A. 2.5
B. 3.5
C. 6
D. 8.5
E. 12

I am getting an answer close to 5. Below are the steps I followed (let me know if something is incorrect):
To till 72 acres of land:
Andy takes = $$\sqrt{72}$$ hours
Bill takes = 10*72/60 = 12 hours
Rate of Andy's work = $$1/\sqrt{72}$$
Rate's of Bill's work = 1/12
Together = $$1/12 + 1/\sqrt{72}$$
Time taken = $$\frac{1}{(1/12 + 1/\sqrt{72} )}$$ = approximately 5 hours

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Re: Andy takes sqrt(x) hours to till x acres of land whereas [#permalink]

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24 Feb 2016, 21:00
ramyatang wrote:
TeamGMATIFY wrote:
Andy takes $$\sqrt{x}$$ hours to till $$x$$ acres of land while Bill takes 10 minutes to till each acre of land. If they work together, approximately how many hours will they take to till 72 acres of land?

A. 2.5
B. 3.5
C. 6
D. 8.5
E. 12

I am getting an answer close to 5. Below are the steps I followed (let me know if something is incorrect):
To till 72 acres of land:
Andy takes = $$\sqrt{72}$$ hours
Bill takes = 10*72/60 = 12 hours
Rate of Andy's work = $$1/\sqrt{72}$$
Rate's of Bill's work = 1/12
Together = $$1/12 + 1/\sqrt{72}$$
Time taken = $$\frac{1}{(1/12 + 1/\sqrt{72} )}$$ = approximately 5 hours

Hi,
where you are going wrong is that you are taking the hourly work as constant..NO
if he was doing entire 72 acres than his speed would be $$1/\sqrt{72}$$..
so his hourly work is dependent on the acreage he has to do..

here best would be to test the numbers..
1) first see what work is done by B in those hours and then check if the remaining acres and speed of A is as given by the equation $$\sqrt{x}$$..

it cannot be 12 and 6 seems the most sensible number...
ofcourse you may start from one end..
lsts see what happens in 6 hours..
B does 6*6=36 acres..
So A does remaining 72-36, 36 , in $$\sqrt{36}$$ in 6hours, which matches
so ans is 6..

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Re: Andy takes sqrt(x) hours to till x acres of land whereas [#permalink]

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24 Feb 2016, 21:47
Expert's post
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TeamGMATIFY wrote:
Andy takes $$\sqrt{x}$$ hours to till $$x$$ acres of land while Bill takes 10 minutes to till each acre of land. If they work together, approximately how many hours will they take to till 72 acres of land?

A. 2.5
B. 3.5
C. 6
D. 8.5
E. 12

Hi,
since the speed of A varies with the acreage he does, we cannot talk of one our work being constant..
B does 1 acre in 10 min or 6 acres per hour

Now, let A do x acres out of 72 in $$\sqrt{x}$$ hrs..
B will do the remaining work 72-x in (72-x)/6 hrs..
but both A and B have worked together and for same time..
so $$\sqrt{x}$$ =(72-x)/6 ..
=> 6$$\sqrt{x}$$ =(72-x)..
=> $$\sqrt{x}^2$$+6$$\sqrt{x}$$ -72=0..
=> $$\sqrt{x}^2$$+12$$\sqrt{x}$$-6$$\sqrt{x}$$ -72=0..
=> ( $$\sqrt{x}$$+12)( $$\sqrt{x}$$-6)=0..
so $$\sqrt{x}$$= -12 or 6..
As hour has to be a positive number , 6 is the answer
C
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Re: Andy takes sqrt(x) hours to till x acres of land whereas [#permalink]

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Re: Andy takes sqrt(x) hours to till x acres of land whereas [#permalink]

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13 May 2017, 11:25
chetan2u wrote:
TeamGMATIFY wrote:
Andy takes $$\sqrt{x}$$ hours to till $$x$$ acres of land while Bill takes 10 minutes to till each acre of land. If they work together, approximately how many hours will they take to till 72 acres of land?

A. 2.5
B. 3.5
C. 6
D. 8.5
E. 12

Hi,
since the speed of A varies with the acreage he does, we cannot talk of one our work being constant..
B does 1 acre in 10 min or 6 acres per hour

Now, let A do x acres out of 72 in $$\sqrt{x}$$ hrs..
B will do the remaining work 72-x in (72-x)/6 hrs..
but both A and B have worked together and for same time..
so $$\sqrt{x}$$ =(72-x)/6 ..
=> 6$$\sqrt{x}$$ =(72-x)..
=> $$\sqrt{x}^2$$+6$$\sqrt{x}$$ -72=0..
=> $$\sqrt{x}^2$$+12$$\sqrt{x}$$-6$$\sqrt{x}$$ -72=0..
=> ( $$\sqrt{x}$$+12)( $$\sqrt{x}$$-6)=0..
so $$\sqrt{x}$$= -12 or 6..
As hour has to be a positive number , 6 is the answer
C

Hi chetan2u

is this a GMAT like question?
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Andy takes sqrt(x) hours to till x acres of land whereas [#permalink]

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14 May 2017, 08:34
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TeamGMATIFY wrote:
Andy takes $$\sqrt{x}$$ hours to till $$x$$ acres of land while Bill takes 10 minutes to till each acre of land. If they work together, approximately how many hours will they take to till 72 acres of land?

A. 2.5
B. 3.5
C. 6
D. 8.5
E. 12

You can solve this question by testing the options.

A. 2.5 hours
Bill will till 15 acres so remaining 57 not a perfect square ..

B. 3.5
Bill will till 21 acres, so remaining 51.. not a perfect square..

C. 6
Bill will till 36 acres.. remaining 36 acres will be tilled by Andy in$$\sqrt{36}$$ = 6 hours

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Re: Andy takes sqrt(x) hours to till x acres of land whereas [#permalink]

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04 Aug 2017, 07:29
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TeamGMATIFY wrote:
Andy takes $$\sqrt{x}$$ hours to till $$x$$ acres of land while Bill takes 10 minutes to till each acre of land. If they work together, approximately how many hours will they take to till 72 acres of land?

A. 2.5
B. 3.5
C. 6
D. 8.5
E. 12

Lengthy Process : Algebraic approach

Let x acre is tilled by Andy and 72-x acre is tilled by Bill.
So, time taken by Andy = $$\sqrt{x}$$
In this $$\sqrt{x}$$ time Bill tilled 72-x acre of land.
Also to till 72-x acre of land Bill will take (72-x)*10/60 hours = (72-x)/6 hours.

So, $$\sqrt{x}$$ = (72-x)/6
6*$$\sqrt{x}$$ = (72-x)
36 x = 72^2 + x^2 -144x
x^2 -144 x -36x +72^2 = 0
x(x-144) -36(x-144) = 0
x= 144, 36

But x can't be greater than 72 . So, x = 36
$$\sqrt{x}$$ = 6.

Shorter Process : GMAT Approach
Start putting options to check if the time taken by Bill matches with the both ways.
Option 1: time taken = 2.5
Land tilled by Andy = 6.25
Land tilled by Bill = 65.75 Time taken =65.75/6= approx 10+ =/=2.5

Option 2: time taken = 3.5
Land tilled by Andy = 12.25
Land tilled by Bill = 59.75 Time taken =59.75/6= approx 10- =/=3.5

Option 3: time taken = 6
Land tilled by Andy = 36
Land tilled by Bill = 36 Time taken = approx 36/6 =6 same as the option....

All GMAT takers should learn to try this approach..

Appreciate if you like my solution..
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Re: Andy takes sqrt(x) hours to till x acres of land whereas   [#permalink] 04 Aug 2017, 07:29
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