Drill Press M can bore 3000 holes an hour and Drill Press N can bore 2500 holes an hour. If the two machines together must bore 45,000 holes, and if each machine can operate for at most 9 hours, what is the least amount of time, in hours, Drill Press N must operate?
A. 6
B. 7
C. 36/7
D. 8
E. 90/11
The OA is C.
I'm really confused by this PS question. Experts, any suggestion about how to solve it? Thanks in advance.
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Drill Press M can bore 3000 holes an hour and Drill Press...
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BTGmoderatorLU
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Hello LUANDATO.LUANDATO wrote:Drill Press M can bore 3000 holes an hour and Drill Press N can bore 2500 holes an hour. If the two machines together must bore 45,000 holes, and if each machine can operate for at most 9 hours, what is the least amount of time, in hours, Drill Press N must operate?
A. 6
B. 7
C. 36/7
D. 8
E. 90/11
The OA is C.
I'm really confused by this PS question. Experts, any suggestion about how to solve it? Thanks in advance.
There is a mistake with the option C. The correct answer should be 36/5. Let's see why.
We know that Drill Press M has to operate for 9 hours (in this way, the number of hours that has to operate Drill Press N will be minimum). Hence, Drill Press M will bore 3000*9 = 27.000 holes.
Now, Drill Press N has to bore 45.000-27.000 = 18.000 holes.
The time that Drill Press N has to operate is 18.000 / 2.500 = 180 / 25 = 36/5 hours.
This is why the correct answer is 36/5 hours.
I hope this explanation may help you.
Feel free to ask me again if you have a doubt.
Regards.
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We are given that the rate of Drill Press M is 3000 holes/hour and the rate of Drill Press N is 2500 holes/hour. Since each machine can operate for at most 9 hours and we need to determine the minimum number of hours of operating time for N, we can let M work for 9 hours, and thus 3000 x 9 = 27,000 holes are completed, leaving 45,000 - 27,000 = 18,000 holes to be completed by N.BTGmoderatorLU wrote:Drill Press M can bore 3000 holes an hour and Drill Press N can bore 2500 holes an hour. If the two machines together must bore 45,000 holes, and if each machine can operate for at most 9 hours, what is the least amount of time, in hours, Drill Press N must operate?
A. 6
B. 7
C. 36/7
D. 8
E. 90/11
Since time = work/rate, N must operate for 18,000/2,500 = 180/25 = 36/5 hours. (Note the typo for choice C, which should be 36/5.)
Answer: C
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