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29 Jan 2024, 02:38
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D
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Working together at their respective constant rates, machine R, machine S, and machine T can produce a batch of parts in 4 hours. If machine R, working alone at its constant rate, can produce the same batch of parts in 6 hours, how many hours would it take machine S and machine T, working together at their respective constant rates, to produce the same batch of parts?
A. 6
B. 8
C. 10
D. 12
E. 14
2024-01-29_13-37-02.png [ 54.01 KiB | Viewed 5029 times ]
A. 6
B. 8
C. 10
D. 12
E. 14
Attachment:
2024-01-29_13-37-02.png [ 54.01 KiB | Viewed 5029 times ]
29 Jan 2024, 02:41
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guddo
Assuming the rates of machines R, S, and T are r, s, and t, respectively, we are given:
- r + s + t = 1/4 and r = 1/6.
Subtracting the second equation from the first results in:
- s + t = 1 = 1/4 - 1/6 = 1/12.
Since rate is the reciprocal of time, machine S and machine T, would take 12 hours to produce the same batch of parts.
Answer: D.
20 Dec 2024, 11:37
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Say, Total work = 24 units
R + S + T = 6 units / hour
R = 24/6 = 4 units / hour
S+ T = 2 units/ hour
S and T would need= 24/2 = 12 hours
R + S + T = 6 units / hour
R = 24/6 = 4 units / hour
S+ T = 2 units/ hour
S and T would need= 24/2 = 12 hours
