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GMATPrep: A farm used two harvesting

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by NandishSS » Wed Sep 13, 2017 7:09 am
A farm used two harvesting machines, H and K, to harvest 100 acres of wheat. Harvesting machine H, working alone at its constant rate, harvested 40 acres of wheat in 8 hours. Then harvesting machine K was brought in, and harvesting machines H and K, working together at their respective constant rates, harvested the remaining acres of wheat in 5 hours. Harvesting machine K harvested how many acres of wheat per hour?

(A) 7
(B) 8
(C) 12
(D) 13
(E) 15

OA: A
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by DavidG@VeritasPrep » Wed Sep 13, 2017 7:26 am
NandishSS wrote:A farm used two harvesting machines, H and K, to harvest 100 acres of wheat. Harvesting machine H, working alone at its constant rate, harvested 40 acres of wheat in 8 hours. Then harvesting machine K was brought in, and harvesting machines H and K, working together at their respective constant rates, harvested the remaining acres of wheat in 5 hours. Harvesting machine K harvested how many acres of wheat per hour?

(A) 7
(B) 8
(C) 12
(D) 13
(E) 15

OA: A
Let's call K's rate 'k' and H's rate 'h.'
We know h = 40 acres/8 hours = 5 acres/hour.

If h does 40 acres on its own, then there are 60 acres left to do. If those 60 acres are completed by both machines in 5 hours, then the combined rate is 60 acres/5 hours = 12 acres hour.

Because rates are additive in work problems, we now know that k + h = 12 or k + 5 = 12, so k = 7. The answer is A
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by NandishSS » Wed Sep 13, 2017 7:50 am
How to deal with this kind of problems? I just bogged down seeing this...

Any link to deal with Word Problems & Work rate problem
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by DavidG@VeritasPrep » Wed Sep 13, 2017 9:03 am
NandishSS wrote:How to deal with this kind of problems? I just bogged down seeing this...

Any link to deal with Word Problems & Work rate problem
You might find this post helpful: https://www.veritasprep.com/blog/2016/0 ... omponents/
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by Scott@TargetTestPrep » Wed Sep 20, 2017 2:36 pm
NandishSS wrote:A farm used two harvesting machines, H and K, to harvest 100 acres of wheat. Harvesting machine H, working alone at its constant rate, harvested 40 acres of wheat in 8 hours. Then harvesting machine K was brought in, and harvesting machines H and K, working together at their respective constant rates, harvested the remaining acres of wheat in 5 hours. Harvesting machine K harvested how many acres of wheat per hour?

(A) 7
(B) 8
(C) 12
(D) 13
(E) 15
The rate of harvesting machine H is 40/8 = 5 acres per hour.

We can let the rate of harvesting machine K = k acres per hour.

Thus, the combined rate of machines K and H is 5 + k, and we are given that they harvest 60 acres in 5 hours; thus:

(5 + k) x 5 = 60

5 + k = 12

k = 7

Answer: A

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