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Machine R, working alone at a constant rate, produces x unit [#permalink]
06 Dec 2015, 16:44
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Machine R, working alone at a constant rate, produces x units of a product in 30 minutes, and machine S, working alone at a constant rate, produces x units of the product in 48 minutes, where x is a positive integer.
Quantity A 
Quantity B 
The number of units of the product that machine R, working alone at its constant rate, produces in 3 hours 
The number of units of the product that machine S, working alone at its constant rate, produces in 4 hours 
A)The quantity in Column A is greater. B)The quantity in Column B is greater. C)The two quantities are equal. D)The relationship cannot be determined from the information given. Practice Questions Question: 1 Page: 150 Difficulty: medium
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Re: Machine R, working alone at a constant rate, produces x unit [#permalink]
06 Dec 2015, 16:47
Explanation Let X is 1. Number of units by A in 3 hours = \(\frac{180 min}{30 min}\)= 6 Number of units by B in 4 hours = \(\frac{240 min}{48 min}\)= 5 Hence, option \(A\) is greater.
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Re: Machine R, working alone at a constant rate, produces x unit [#permalink]
05 Jun 2018, 10:10
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sandy wrote: Machine R, working alone at a constant rate, produces x units of a product in 30 minutes, and machine S, working alone at a constant rate, produces x units of the product in 48 minutes, where x is a positive integer.
Quantity A 
Quantity B 
The number of units of the product that machine R, working alone at its constant rate, produces in 3 hours 
The number of units of the product that machine S, working alone at its constant rate, produces in 4 hours 
IMPORTANT: When solving work questions, we must make sure that the values all feature the same units of measurement. For example, if our rate is expressed as units per MINUTE, then our time should also be in MINUTES. Conversely, if our rate is expressed as units per HOUR, then our time should also be in HOUR. Let's go with MINUTES ASIDE Rule: If a person can complete an entire job in k hours, then in one hour, the person can complete 1/k of the jobExample: If it takes Sue 5 hours to complete a job, then in one hour, she can complete 1/5 of the job. In other words, her work rate is 1/5 of the job per hour  Output = (rate)(time)We know the work times are 3 hours (aka 180 MINUTES) and 4 hours (aka 240 MINUTES) So, let's determine the rates for each machine. Machine R, working alone at a constant rate, produces x units of a product in 30 minutesSo, in ONE MINUTE, machine R can produce x/30 units In other words, machine R's RATE is x/30 units PER MINUTE Machine S, working alone, produces x units of the product in 48 minutesSo, in ONE MINUTE, machine S can produce x/48 units In other words, machine S's RATE is x/40 units PER MINUTE QUANTITY A: The number of units of the product that machine R, working alone at its constant rate, produces in 3 hours (aka 180 MINUTES) Output = (rate)(time) = ( x/30 units PER MINUTE)(180 MINUTES) = 180x/30 = 6x QUANTITY B: The number of units of the product that machine S, working alone at its constant rate, produces in 4 hours (aka 240 MINUTES) Output = (rate)(time) = ( x/40 units PER MINUTE)(240 MINUTES) = 240x/48 = 5x So, we have: Quantity A: 6x Quantity B: 5x Since x is POSITIVE, we can see that Quantity A is greater. Answer: A Cheers, Brent
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Re: Machine R, working alone at a constant rate, produces x unit [#permalink]
05 Jun 2018, 16:41
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Answer: A R: x units in 30. Minutes S: x units in 48 minutes
A: How many products in 3 hours? / x units in 0.5 hour. Answer = 3/0.5 * x = 6x B: How many products in 4 hours? / x units in 48/60 hour. Answer = 4 / (48/60) *x = 5x
So A is bigger than B. (The speed of machine A is 48/30=7/5 times faster than B.)
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Re: Machine R, working alone at a constant rate, produces x unit [#permalink]
27 Apr 2020, 12:57
GreenlightTestPrep wrote: sandy wrote: Machine R, working alone at a constant rate, produces x units of a product in 30 minutes, and machine S, working alone at a constant rate, produces x units of the product in 48 minutes, where x is a positive integer.
Quantity A 
Quantity B 
The number of units of the product that machine R, working alone at its constant rate, produces in 3 hours 
The number of units of the product that machine S, working alone at its constant rate, produces in 4 hours 
IMPORTANT: When solving work questions, we must make sure that the values all feature the same units of measurement. For example, if our rate is expressed as units per MINUTE, then our time should also be in MINUTES. Conversely, if our rate is expressed as units per HOUR, then our time should also be in HOUR. Let's go with MINUTES ASIDE Rule: If a person can complete an entire job in k hours, then in one hour, the person can complete 1/k of the jobExample: If it takes Sue 5 hours to complete a job, then in one hour, she can complete 1/5 of the job. In other words, her work rate is 1/5 of the job per hour  Output = (rate)(time)We know the work times are 3 hours (aka 180 MINUTES) and 4 hours (aka 240 MINUTES) So, let's determine the rates for each machine. Machine R, working alone at a constant rate, produces x units of a product in 30 minutesSo, in ONE MINUTE, machine R can produce x/30 units In other words, machine R's RATE is x/30 units PER MINUTE Machine S, working alone, produces x units of the product in 48 minutesSo, in ONE MINUTE, machine S can produce x/48 units In other words, machine S's RATE is x/40 units PER MINUTEQUANTITY A: The number of units of the product that machine R, working alone at its constant rate, produces in 3 hours (aka 180 MINUTES) Output = (rate)(time) = ( x/30 units PER MINUTE)(180 MINUTES) = 180x/30 = 6x QUANTITY B: The number of units of the product that machine S, working alone at its constant rate, produces in 4 hours (aka 240 MINUTES) Output = (rate)(time) = (x/40 units PER MINUTE)(240 MINUTES)= 240x/48 = 5x So, we have: Quantity A: 6x Quantity B: 5x Since x is POSITIVE, we can see that Quantity A is greater. Answer: A Cheers, Brent I think there is a typing mistake? It should be x/48
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Re: Machine R, working alone at a constant rate, produces x unit
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