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

Question

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

RMD007 · Accepted Answer

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

Kudos if helped...

chetan2u · Answer

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

ramyatang · Answer

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

chetan2u · Answer

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..

ShashankDave · Answer

Hi  chetan2u

is this a GMAT like question?

shashankism · Answer

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.... This is the answer... All GMAT takers should learn to try this approach.. Appreciate if you like my solution..

jaykpatel21 · Answer

For such questions, back solving approach is the best option. Considering 72 and taking x^2 into consideration, you should first try the whole numbers. 
6^2 = 36 + 36 (bill) = 72

Posted from my mobile device

sebarm95 · Answer

The way I worked it out was to split the work by the number f workers, ie. 72acres/2 is 36 acres. 
Andy and Bill therefore get 36 acres of land to till, each.

Andy: √x acres =  hours  of work
Bill: No# acres *10 =  mins  of work / 60 = hours of work

Now we plug in the  36 acres  they each get.

Andy: √36 acres = √36 hours of work = 6 hours of work
Bill: 36 acres * 10 = 360 mins of work = 6 hours

Take the sum number of hours worked and divide by the number of people working

6 hours + 6 hours/2 people = 6+6/2 = 12/2 =6

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards