The speed at which a machine operates is directly proportional to

Question

The speed at which a certain machine operates is directly proportional to the square root of the amount of electrical power the machine receives. If the machine receives 900 watts of power for an hour and then 1600 watts of power for two hours, it produces 330 items. How many such items will it produce in three hours if it receives 400 watts of power the entire time?

(A) 60

(B) 110

(C) 180

(D) 240

(E) 330

Source: Marty Murray Coaching

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Official Answer

C

(A) 60

(B) 110

(C) 180

(D) 240

(E) 330

Source:  Marty Murray Coaching

APram · Answer

Speed is directly proportional to square root of power
 S = k\sqrt{P} 
 330 = k (1*\sqrt{900}+ 2*\sqrt{1600}) 
 k=3

S = 3*3*\sqrt{400} 
S = 180
Hence C is correct

TheLegacy · Answer

Square Root of 900 = 30 , Square Root of 1600 = 40 , Square Root of 400 = 20

In the first case, I can imagine having a total speed of 30 + 40 +40 = 110, which gives me an output of 330 items.

In the second case, I can imagine having a total speed of 20 + 20 + 20 = 60, which gives me the unknown output (u) of items.

Now, basic ratios : 330 : 110 = u : 60 -> u = (330 x 60) / 110 = 180 items.

Answer choice (C) is the correct one.

harsh96 · Answer

MartyMurray

how speed has become same as Amount of work here?

GridLock · Answer

Speed is not the same as amount of work. It is mentioned in the question that speed is directly proportional to square root of power supplied.

For the first hour 
Speed  is proportional to sqrt(900) i.e. 30 
 To remove the proportional sign, consider a factor k 
 Speed = 30k 
 Work done = Speed * Time = 30k*1hour = 30k

For the later two hours  
 Speed is proportional to sqrt(1600) i.e. 40 
 To remove the proportional sign, the same factor k will come into picture
Speed = 40k
Work done = Speed * Time = 40k*2hour = 80k

We know that total items produced in 3 hours = work done in first hour + work done in later 2 hours = 330 
 => 30k +80k = 330 
 => 110k = 330 => k =3

For the last part  
 Power supplied = 400W 
 Speed = sqrt(400) * k = 20 * 3 = 60 units per hour 
 Work done = Speed * Time = 60*3 = 180

Thus 180 is the answer.

MartyMurray · Answer

The basic concept we'll use to answer this question is the following:

Rate × Time = Work

So, we need to determine the rate at which the machine works at each level of power received.

The passage says the following:

The speed at which a certain machine operates is directly proportional to the square root of the amount of electrical power the machine receives.

Mathematically, that translates to the following, in which  k  is a constant and  p  is the power received:

Rate  = k\sqrt{p}

If the machine receives 900 watts of power for an hour and then 1600 watts of power for two hours, it produces 330 items.

That translates to the following:

(k\sqrt{900} × 1) + (k\sqrt{1600} × 2) = 330

30k + 80k = 330

k = 3

How many such items will it produce in three hours if it receives 400 watts of power the entire time?

k\sqrt{400} × 3 = (3 × 20) × 3 =180

(A) 60

(B) 110

(C) 180

(D) 240

(E) 330

Correct answer:   C

The speed at which a machine operates is directly proportional to

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