8 identical machines, working alone and at their constant rates, take

Ans: E

Solution: 8 machines take 6 hrs to complete the job, so one machine will take 8*6= 48 hrs to complete the job alone.
three machine together will finish the work in = 48/3 = 16 hrs.
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IMO: E

Let each machine do 1 unit of work for 1 hour
8 machines --> 8 units of work in 1 hour
For 6 hours = 8*6 = 48 Units of total work is done.

Now this 48 Units of total work must be done by 3 machines
3 units of work(3 machines) ---> 1 hour
for 48 Units of work
3*16 ---> 1*16 hours

Thus a total of 16 hours

8 machines take 6 hours for 1 job. Therefore their rate is 1/6. Divide by number of machines 8, and then multiply by 3 to get the rate for 3 machines.

=> \(1/6 * 1/8 = 1/48\)
=> \(1/48 * 3 = 3/48\)

Take the reciprocal for the time taken, 48/3 = 16 Hours

As number of machines reduced it will take more time to complete the same job.
we have to increase the number of hours.
multiply 6 hours with the increasing ratio, that is, 8/3
You get 16 hours.

By using formula
M1D1H1/w1=M2D2H2/w2 we can deduce
8*6 =3*H2
Therefore H2=16
E

A, B and C are out automatically since the number of machines are less than half, and less than half results in more than double the time. Between D and E, option E, for 16 hours is the same amount of hours (48) as the whole 8 needed. Option E.

Kr,
Mejia

Using chain rule, (8 machines*6 hours)/1 job done=(3 machines*no of hours)/1 job done
No of hours=16 hours
Answer E

VERITAS PREP OFFICIAL SOLUTION:

Given that 8 machine rates = 1 job / 6 hours, you can divide both sides of that equation by 8 to find the rate of 1 machine working alone. That means that the rate of one machine is 1 job / 48 hours. Because you have 3 machines, you can multiply that rate by 3 to find the rate of 3 machines, which is then 3 jobs / 48 hours which reduces to 1 job / 16 hours. Therefore it will take 16 hours for 3 machines to perform the job.

A helpful shortcut to this problem is to recognize that the time and the number of machines are inversely proportional (fewer machines will take longer). So since you have 3/8 as many machines, it will take 8/3 as long. 8/3 * 6 = 16, answer choice E.
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Time taken by each machine = 8*1/x = 1/6 . This gives x= 48 hours.
Time taken by 3 machines = 48/3 = 16 hours (E)

The rate for 8 machines is 1/6. Let’s use the following proportion to determine the rate (which we can call n) of 3 machines:

8/(1/6) = 3/n

48 = 3/n

48n = 3

n = 3/48 = 1/16

We see that the rate of 3 machines is 1/16; thus, it will take 3 machines 16 hours to perform the same job.

Answer: E
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8 machines perform 1 job in 6 hours
1 machine performs \(\frac{1}{8}\) th of the job in 6 hours
1 machine performs \(\frac{1}{(8*6)}\) job in 1 hour

Hence rate of 1 machine is \(\frac{1}{48}\)
Rate of 3 machines is \(3*\frac{1}{48}\) = \(\frac{1}{16}\)

or, 3 machines will finish 1 job in 16 hours.

header3]Solution[/header3]

Given

• 8 identical machines, working alone and at their constant rates, take 6 hours to complete a job lot.

To find

• The time 3 such machines will take to perform the same job

Approach and Working out

• Total machine hours required to complete the work = 8* 6 = 48 hours

o 3 machines can complete this work in= 48/3 =16 hour

Thus, option E is the correct answer.
Correct Answer: Option 0045
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8 identical machines, working alone and at their constant rates, take 6 hours to complete a job lot. How long would it take for 3 such machines to perform the same job?

A. 2.25 hours
B. 8.75 hours
C. 12 hours
D. 14.25 hours
E. 16 hours

Correct Answere is E

shouldn't the question read: "8 machines working together..."?

8 identical machines, working alone and at their constant rates, take 6 hours to complete a job lot. How long would it take for 3 such machines to perform the same job?

A. 2.25 hours
B. 8.75 hours
C. 12 hours
D. 14.25 hours
E. 16 hours

8 machines take 6 hours
1 machine takes 8*6 hours
3 machines take (8*6)/3 = 16 hours

Answer: E

Formula of

n1xd1= n2xd2

can be used since the work is the same

8x6=3x
x=16