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
_________________
Brent Hanneson – Creator of greenlighttestprep.com
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