If 5 machines can produce 20 units in 10 hours, how long would it take

Question

If 5 machines can produce 20 units in 10 hours, how long would it take 20 machines to produce 100 units?

A. 50 hours
B. 40 hours
C. 12.5 hours
D. 12 hours
E. 8 hours

thac · Answer

5 machines would produce 100 units in 50 hours. Increasing the amount of machines by 4 would mean dividing 50 hours by 4.

50/4 = 12.5

Ans C

nrmlvrm · Answer

Ans:  100/(((20/10)/5)*20) = 12.5  Hence (C)

EMPOWERgmatRichC · Answer

Hi All,

If you find yourself getting 'lost' in these types of questions, it often helps to 'break down the data step-by-step:

Here, we're told that 5 machines can produce 20 units in 10 hours....

That means that EACH machine WORKS for 10 hours apiece. Since there are 5 machines (and we're meant to assume that each machine does the same amount of work), then the 5 machines equally created the 20 units.

20 units/5 machines = 4 units are made by each machine every 10 hours

Now that we know how long it takes each machine to make 4 units, we can break THIS down further if we choose to...

10 hours/4 units = 2.5 hours per unit when 1 machine is working.

The prompt asks us how long would it take 20 machines to produce 100 units.

If 20 machines each work for 2.5 hours, then we'll have 20 units. Since 100 units is '5 times' 20, we need '5 times' more TIME.

(2.5 hours)(5 times) = 12.5 hours

Final Answer:  C

GMAT assassins aren't born, they're made,
Rich

Mo2men · Answer

We can approach the problem in 2 ways:

1: If you are familiar with this concept, so apply directly
 (M1∗T1)/W1=(M2∗T2)/W2 , where M=machine power, T=time, W=work done

(5*10)/20= 20T/100 , then T=12.5 hrs

2: In case do not know the above formula , then easily to apply quickly as

W =R * T R= W/T= 20/(5*10)

Because Rate is constant, so it equals in both cases 20/(5*10)= 100/20T, T =12.5 hrs

P.S.: Both methods are the same concept.

KrishnakumarKA1 · Answer

work done per machine per hour = 20/5*10 = 0.4
let the time taken be t
therefore 0.4*20*t = 100
t = 12.5 hours

generis · Answer

If you like the formula (R*T= W), just add 
(# of machines) to LHS. If you are fluent with RT = W, solving takes well under a minute

(1)  Find rate of an individual machine from

Scenario #1:
# of machines: 5
Rate: ?? units/hour
Time: 10 hours
Work finished: 20 units

(# of machines) * R * T = W 
  5 * R * 10 = 20  
 R = \frac{20}{5*10}=\frac{2}{5}

(2)  Scenario #2 - use rate plus equation to find time in new scenario

At individual machine rate of  \frac{2}{5} , how long will 20 machines require to make 100 units?

(# of machines) * R * T = W 
  20*\frac{2}{5}*T=100 
 8*T=100  
 T=\frac{100}{8}=12.5  hours

Answer C

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If 5 machines can produce 20 units in 10 hours, how long would it take

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If 5 machines can produce 20 units in 10 hours, how long would it take

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