A farm used two harvesting machines, H and K, to harvest 100 acres of wheat. Harvesting machine H, working alone...

BTGmoderatorLU wrote: ↑

Sun Dec 27, 2020 8:43 am

Source: GMAT Prep

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 OA is A

Solution:

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

Alternate Solution:

Machine H harvests 40 acres in 8 hours; thus, it harvests 40/8 = 5 acres per hour. It would take the same machine 60/5 = 12 hours to harvest the remaining 100 - 40 = 60 acres.

We are given that machines H and K working together can harvest 60 acres in 5 hour; therefore, in one hour, they complete 1/5 of the 60 acres. Since machine H does the same job alone in 12 hours, it completes 1/12 of the 60 acres in one hour. Thus, machine K alone can complete 1/5 - 1/12 = 12/60 - 5/60 = 7/60 of the 60 acres. Then, it takes machine K 60/7 hours to harvest 60 acres, and in one hour, machine K can harvest 60/(60/7) = 7 acres.

Answer: A