One machine, working at a constant rate, can fill a production order in 8 hours. How long would it take four identical machines, working at the same constant rate, to fill the order?
A. 2 hours
B. 4 hours
C. 8 hours
D. 16 hours
E. 32 hours
The OA is A.
Source: Veritas Prep
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One machine, working at a constant rate, can fill a certain
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fskilnik@GMATH
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<p>
The solution above follows the notations and rationale taught in the <b>GMATH</b> method.
It suffices to apply the generalization of the "taps shortcut", valid for any (finite) number of "taps".swerve wrote:</p>
One machine, working at a constant rate, can fill a production order in 8 hours. How long would it take four identical machines, working at the same constant rate, to fill the order?
A. 2 hours
B. 4 hours
C. 8 hours
D. 16 hours
E. 32 hours
The solution above follows the notations and rationale taught in the <b>GMATH</b> method.
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Let's assign a "nice" value to the entire job (a value that works well with the given information)swerve wrote:One machine, working at a constant rate, can fill a production order in 8 hours. How long would it take four identical machines, working at the same constant rate, to fill the order?
A. 2 hours
B. 4 hours
C. 8 hours
D. 16 hours
E. 32 hours
The OA is A.
Source: Veritas Prep
Let's say the machine is making widgets and an order = 8 widgets.
One machine, working at a constant rate, can fill a production order in 8 hours.
In other words, ONE machine can make 8 widgets in 8 hours
This means, ONE machine makes 1 widget per hour
How long would it take four machines to fill the order?
If ONE machine makes 1 widget in ONE hour,
then FOUR machines makes 4 widgets in ONE hour,
which means FOUR machines makes 8 widgets in TWO hours
Answer: A
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Brent
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GMATGuruNY
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Time and rate have a RECIPROCAL RELATIONSHIP.
If Mary works TWICE as fast as John, Mary's time will be 1/2 John's time.
If Mary works THREE TIMES as fast as John, Mary's time will be 1/3 John's time
(1/4)(8) = 2 hours.
The correct answer is A.
If Mary works TWICE as fast as John, Mary's time will be 1/2 John's time.
If Mary works THREE TIMES as fast as John, Mary's time will be 1/3 John's time
Since 4 machines will work 4 times as fast as 1 machine, the time for 4 machines will be 1/4 the time for 1 machine:swerve wrote:One machine, working at a constant rate, can fill a production order in 8 hours. How long would it take four identical machines, working at the same constant rate, to fill the order?
A. 2 hours
B. 4 hours
C. 8 hours
D. 16 hours
E. 32 hour
(1/4)(8) = 2 hours.
The correct answer is A.
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Since the rate of 1 machine is 1/8, the rate of 4 machines is 4/8 = 1/2.swerve wrote:One machine, working at a constant rate, can fill a production order in 8 hours. How long would it take four identical machines, working at the same constant rate, to fill the order?
A. 2 hours
B. 4 hours
C. 8 hours
D. 16 hours
E. 32 hours
Thus, it will take 4 machines 1/(1/2) = 2 hours to fill the order.
Answer: A
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