If it is assumed that each of the n production workers in a factory as

Question

If it is assumed that each of the n production workers in a factory assembles one instrument every t minutes, how many instruments does the factory assemble in 7.5 hours of production?

A.  \frac{450n}{t}

B.  \frac{450t}{n}

C.  450nt

D.  \frac{7.5tn}{60}

E.  \frac{7.5n}{60t}

AkshdeepS · Accepted Answer

Rate of 1 worker = \frac{1}{t}

Say, work =  W

Then, Workers * Rate * Time = Total Work

n * \frac{1}{t} * 7.5 = W

\frac{450n}{t}  = W

Hence A

Gladiator59 · Answer

One worker assembles 1 instrument in t minutes.

One worker assembles 60/t instruments in one hour. ( Unitary method or if you put t = 60 mins it comes to 1 instrument per hour)

One worker assembles 60/t * 7.5 instruments in given time.

One worker assembles 450 / t instruments then n workers would n times that or 450n/t instruments.

Hence Option (A) is our choice.

Best,
Gladi

KarishmaB · Answer

Another option is to assume values. Say 1 worker assembles 1 instrument in 30 mins (t = 30).
In 7.5 hrs, 1 worker will assemble 15 instruments. 
Put n = 1 and t = 30 in options. You should get 15 from the correct answer.

Only option (A) gives you 15.

nguyenkhanhlinh · Answer

I want to ask for a moment why 1 / t is the worker ratio
and "Workers * Rate * Time = Total Work" Can you tell me about this , it seems the shortest and easiest to do

AkshdeepS · Answer

Alright ,

1 worker is cutting 60 apples in 60 minutes. What will be his rate of cutting?

Work = Time * Rate * No. of workers

Rate = Work / (Time * No. of workers)

Rate = 60 / (60 * 1)

Rate = 1/1 or 1 apple per minute

But time is given as "t" in the question and not exactly in minutes or hours.

Therefore, Rate =  \frac{1(work-instrument) }{

MartyMurray · Answer

If it is assumed that each of the n production workers in a factory assembles one instrument every t minutes, how many instruments does the factory assemble in 7.5 hours of production?

We can start by glancing at the answer choices to get a sense of how the correct answer must look. Doing so, we see that some choices use the number 450 while others use 7.5 and 60. If we think about what we're seeing, we can notice that 450 = 7.5 × 60. So, 450 is the number of minutes in 7.5 hours.

Having gotten a sense of the format of the correct answer, we can proceed efficiently as follows:

Rate of one worker: one instrument every t minutes  = \frac{1}{t}

Production of one worker in 7.5 hours, i.e., 450 minutes:  450 × \frac{1}{t} = \frac{450}{t}

Total production of n workers in 450 minutes:  n × \frac{450}{t} = \frac{450n}{t}

A.  \frac{450n}{t}

B.  \frac{450t}{n}

C.  450nt

D.  \frac{7.5tn}{60}

E.  \frac{7.5n}{60t}

Correct answer:   A

If it is assumed that each of the n production workers in a factory as

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