24 computer hackers can scan and infect 10 computers in 5 hours. If this group of hackers wants to scan and infect 20 computers in 8 hours, how many new computers hackers do they need to recruit and join their team in order to accomplish this task, assuming all hackers work at the same rate?
A) 0
B) 6
C) 8
D) 10
E) 16
The OA is the option B.
What equations should in order to solve this PS question? Can someone give me some help? Please.
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24 computer hackers can scan and infect 10 computers in
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Hi VJesus12,
I solved it in the following way,
24 Hackers work at a rate of 10/5 ==> R = 2
X hackers work at a rate of 20/8 ==> R = 5/2
Set up a proportion
(2/1)/24 = (5/2)/X
1/12 = 5/2X
Cross multiplying we get X = 30 and number of additional Hackers would be 30 - 24 = 6. Option B.
Rgeards!
I solved it in the following way,
24 Hackers work at a rate of 10/5 ==> R = 2
X hackers work at a rate of 20/8 ==> R = 5/2
Set up a proportion
(2/1)/24 = (5/2)/X
1/12 = 5/2X
Cross multiplying we get X = 30 and number of additional Hackers would be 30 - 24 = 6. Option B.
Rgeards!
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Use the following equation:VJesus12 wrote:24 computer hackers can scan and infect 10 computers in 5 hours. If this group of hackers wants to scan and infect 20 computers in 8 hours, how many new computers hackers do they need to recruit and join their team in order to accomplish this task, assuming all hackers work at the same rate?
A) 0
B) 6
C) 8
D) 10
E) 16
(workers)(time) / output = (workers)(time) / output
In the equation above:
Workers and time are INVERSELY PROPORTIONAL.
As the number of workers increases, the amount of time required to produce the same output decreases.
Workers and output are DIRECTLY PROPORTIONAL.
As the number of workers increases, the amount of output also increases.
Time and output are also DIRECTLY PROPORTIONAL.
As the amount of time increases, the amount of output also increases.
In the problem above:
(24 hackers)(5 hours)/(10 computers) = (x hackers)(8 hours)/(20 computers)
12 = (2/5)x
60 = 2x
x = 30.
The number of hackers increases from 24 to 30.
Thus:
Number of additional hackers = 30-24 = 6.
The correct answer is B.
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As a tutor, I don't simply teach you how I would approach problems.
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We are given that the rate of 24 computer hackers is 10/5 = 2.VJesus12 wrote:24 computer hackers can scan and infect 10 computers in 5 hours. If this group of hackers wants to scan and infect 20 computers in 8 hours, how many new computers hackers do they need to recruit and join their team in order to accomplish this task, assuming all hackers work at the same rate?
A) 0
B) 6
C) 8
D) 10
E) 16
We need the new rate to be 20/8 = 5/2. We can let x = the number of computer hackers needed to achieve that rate and create the following proportion:
24/2 = x/(5/2)
12 = x/(5/2)
12 = 2x/5
60 = 2x
x = 30
So, the number of new hackers needed is 30 - 24 = 6.
Answer: B
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