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03 Dec 2018, 04:46
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B
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89% (01:36) correct
11%
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Machine A, working alone at its constant rate, produces x pounds of peanut butter in 12 minutes. Machine B, working alone at its constant rate, produces x pounds of peanut butter in 18 minutes. How many minutes will it take machines A and B, working simultaneously at their respective constant rates, to produce x pounds of peanut butter?
A. 7
B. 7.2
C. 7.4
D. 7.5
E. 7.8
A. 7
B. 7.2
C. 7.4
D. 7.5
E. 7.8
Archit3110
Major Poster
03 Dec 2018, 05:35
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Bunuel
A rate: x/12 and B : x/18
Combined rate : 30x/216
10x/72
x= 7.2 IMO B
03 Dec 2018, 10:46
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Bunuel
Another approach is to assign a nice value to x
Let's choose a value that works well 12 minutes and 18 minutes.
So, let's say x = 36
Machine A, working alone at its constant rate, produces x pounds of peanut butter in 12 minutes
In other words, Machine A produces 36 pounds of peanut butter in 12 minutes
So, Machine A's RATE = 3 pounds per minute
Machine B, working alone at its constant rate, produces x pounds of peanut butter in 18 minutes.
In other words, Machine B produces 36 pounds of peanut butter in 18 minutes
So, Machine B's RATE = 2 pounds per minute
How many minutes will it take machines A and B, working simultaneously at their respective constant rates, to produce x pounds (36 pounds) of peanut butter?
COMBINED RATE = 3 pounds per minute + 2 pounds per minute = 5 pounds per minute
Time = output/rate
So, time = 36/5 = 7.2 minutes
Answer: B
Cheers,
Brent
