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# Machine R, working alone at a constant rate, produces x unit

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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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Question Stats:

82% (01:03) correct 17% (00:42) wrong based on 67 sessions
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 ofthe product that machineR, working alone at itsconstant rate, producesin 3 hours The number of units ofthe product that machineS, working alone at itsconstant rate, producesin 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
[Reveal] Spoiler: OA

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Joined: 07 Jun 2014
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GRE 1: Q167 V156
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Kudos [?]: 1895 [0], given: 397

Re: Machine R, working alone at a constant rate, produces x unit [#permalink]  06 Dec 2015, 16:47
Expert's post

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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Expert's post
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 ofthe product that machineR, working alone at itsconstant rate, producesin 3 hours The number of units ofthe product that machineS, working alone at itsconstant rate, producesin 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 job
Example: 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 minutes
So, 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 minutes
So, 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.

Cheers,
Brent
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Re: Machine R, working alone at a constant rate, produces x unit [#permalink]  05 Jun 2018, 16:41
1
KUDOS
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] 05 Jun 2018, 16:41
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