work rate

Question

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sahilchaudhary · Answer

Let (15 Type A & 7 Type B) = x
So, x can do a work in 4 hours.

Let (8 Type B & 15 Type B) = y
So, y can do that work in 11 hours.

So, x & y together can do that work in x*y/(x+y) = 44/15 hours.
Breaking x & y, it gives 15 Type A, 15 Type B & 15 Type C can do that work in 44/15 hours.
So 1 Type A, 1 Type B & 1 Type C can do it 44 hours.

P.S. - I have done this question for the first time.
I got a clue do this question from the fact that 8 Type A and 7 Type B make 15 Type B. Also, 15 Type A and 15 Type C were already provided in the question.

Hope that helps!

Sahil Chaudhary
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GMATGuruNY · Answer

Let the job = 44 units.

Since 15 Type A machines and 7 Type B machines take 4 hours to complete the job, the rate for 15 Type A machines and 7 Type B machines = w/r = 44/4 = 11 units per hour.
Since 8 Type B machines and 15 Type C machines take 11 hours to complete the job, the rate for 8 Type B machines and 15 Type C machines = w/r = 44/11 = 4 units per hour.

Rates can be ADDED together.
Adding together the resulting rates, we get:
(15 Type A + 7 Type B) + (8 Type B + 15 Type C) = (11+4) units per hour
15 Type A + 15 Type B + 15 Type C = 15 units per hour
Type A + Type B + Type C = 1 unit per hour.

Thus:
Time for (Type A + Type B + Type C) to complete the job = w/r = 44/1 = 44 hours.

The correct answer is C.

theCodeToGMAT · Answer

An orthodox approach:

Let Rate of ONE Machine A = A
Let Rate of ONE Machine B = B
Let Rate of ONE Machine C = C

1/4 = 15/A + 7/B --(1)

1/11 = 8/B + 15/C --(2)

Add (1) & (2)

11+4/(44) = 15 ( 1/A + 1/B + 1/C)

So, 44

Answer [spoiler]{C}[/spoiler]

Brent@GMATPrepNow · Answer

Let A = fraction of job that Machine A can complete in 1 hour
Let B = fraction of job that Machine B can complete in 1 hour
Let C = fraction of job that Machine C can complete in 1 hour

15 A Machines and 7 B Machines take 4 hours to complete job
So, in 1 hour, 15 A Machines and 7 B Machines will complete 1/4 of job
In other words, 15A + 7B = 1/4 of job

8 B Machines and 15 C Machines take 11 hours to complete job
So, in 1 hour, 8 B Machines and 15 C Machines will complete 1/11 of job
In other words, 8B + 15C = 1/11 of job

If BOTH GROUPS WORK TOGETHER, we see that, in 1 hour, (15 A Machines and 7 B Machines) + (8 B Machines and 15 C Machines) will complete (1/4 + 1/11) of job

In other words, add 15A + 7B = 1/4 of job and 8B + 15C = 1/11 of job, to get: 15A + 15B + 15C = 15/44
This means that, in 1 hour, 15 A Machines, 15 B Machines, and 15 C Machines can complete 15/44 of the job.

Divide both sides by 15 to get A + B + C = 1/44
This means that, in 1 hour, 1 A Machine, 1 B Machine, and 1 C Machine can complete 1/44 of the job.
So, it will take 44 hours for 1 A Machine, 1 B Machine, and 1 C Machine to complete the job.

Answer: C

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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