Problem Solving

Hi All,

We're told that 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. We're asked for Machine K's harvesting rate in acres of wheat per hour. While this question is wordy, it just comes down to some basic note-taking and Arithmetic.

Since Machine H harvested 40 acres in 8 hours, we know that H's harvesting rate is 40/8 = 5 acres/hour

Machine H and Machine K then harvested together for 5 hours:
Machine H harvested (5)(5 acres/hour) = 25 acres
In total, Machine H harvested 40+25 = 65 of the 100 total acres, which leaves 35 acres for Machine K to harvest over those 5 hours.
Machine K = 35 acres/5 hours = 7 acres/hour

Final Answer: A

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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