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A factory finds that 12 machines, running for 5 hours, can produce 300
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21 Aug 2026, 11:07
21 Aug 2026, 11:07
Expert Reply
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Question Stats:
80% (02:05) correct
20% (02:39) wrong based on 5 sessions
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A factory finds that 12 machines, running for 5 hours, can produce 300 pairs of boots, with every machine operating at the same rate. In a separate production run, 20 machines (at that same rate) begin working, and after 2 hours, 10 additional machines join them. If the machines continue together until they have collectively produced 500 pairs of boots, how many total hours, measured from the start, does the entire production run take?
(A) \(3\)
(B) \(\frac{10}{3} \)
(C) \(4\)
(D) \(5\)
(E) \(\frac{16}{3}
\)
(A) \(3\)
(B) \(\frac{10}{3} \)
(C) \(4\)
(D) \(5\)
(E) \(\frac{16}{3}
\)
- Part of the project: GRE Daily Quant Challenge ALL 4 CORE QUANT AREAS
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Re: A factory finds that 12 machines, running for 5 hours, can produce 300
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29 Aug 2026, 11:22
29 Aug 2026, 11:22
1
Expert Reply
Solution
Rate per machine per hour
12 machines * 5 hours = 60 machine-hours
They produce 300 pairs, so:
\(\text{Rate}=\frac{300}{60}=5\)
Each machine produces 5 pairs per hour.
First 2 hours: 20 machines work for 2 hours:
\(20(2)(5)=200\)
So 200 pairs are produced in the first 2 hours.
Remaining:
500-200=300
After 2 hours
10 additional machines join, so:
\(20+10=30\text{ machines}\)
30 machines produce:
\(30(5)=150\text{ pairs/hour}\)
Time needed for the remaining 300 pairs:
\(\frac{300}{150}=2\text{ hours}\)
Total time
2+2= 4 hours
Answer: C
Rate per machine per hour
12 machines * 5 hours = 60 machine-hours
They produce 300 pairs, so:
\(\text{Rate}=\frac{300}{60}=5\)
Each machine produces 5 pairs per hour.
First 2 hours: 20 machines work for 2 hours:
\(20(2)(5)=200\)
So 200 pairs are produced in the first 2 hours.
Remaining:
500-200=300
After 2 hours
10 additional machines join, so:
\(20+10=30\text{ machines}\)
30 machines produce:
\(30(5)=150\text{ pairs/hour}\)
Time needed for the remaining 300 pairs:
\(\frac{300}{150}=2\text{ hours}\)
Total time
2+2= 4 hours
Answer: C
gmatclubot
Re: A factory finds that 12 machines, running for 5 hours, can produce 300 [#permalink]
29 Aug 2026, 11:22
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