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26 Apr 2026, 13:42
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A warehouse is equipped with identical packing machines, each operating at the same constant rate. If 12 of these machines can package a shipment in \(x\) hours, how many hours would it take y of these machines to package the same shipment?
(1) \(y = 3x\)
(2) One machine can package the shipment in 60 hours.
(1) \(y = 3x\)
(2) One machine can package the shipment in 60 hours.
26 Apr 2026, 13:42
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Official Solution:
A warehouse is equipped with identical packing machines, each operating at the same constant rate. If 12 of these machines can package a shipment in \(x\) hours, how many hours would it take \(y\) of these machines to package the same shipment?
Let's measure the total work in machine hours:
If 12 machines finish in \(x\) hours, total work = \(12 * x\).
If \(y\) machines do the same work, required time = \(\frac{12 * x}{y}\).
(1) \(y = 3x\)
Then required time = \(\frac{12 * x}{3 * x} = 4\) hours. Sufficient.
(2) One machine can package the shipment in 60 hours.
1 machine finishes in 60 hours, so total work = 60 machine hours. Then \(12 * x = 60\), so \(x = 5\). But \(y\) is still unknown, so \(\frac{12 * x}{y}\) is not fixed. Not sufficient.
Answer: A
A warehouse is equipped with identical packing machines, each operating at the same constant rate. If 12 of these machines can package a shipment in \(x\) hours, how many hours would it take \(y\) of these machines to package the same shipment?
Let's measure the total work in machine hours:
If 12 machines finish in \(x\) hours, total work = \(12 * x\).
If \(y\) machines do the same work, required time = \(\frac{12 * x}{y}\).
(1) \(y = 3x\)
Then required time = \(\frac{12 * x}{3 * x} = 4\) hours. Sufficient.
(2) One machine can package the shipment in 60 hours.
1 machine finishes in 60 hours, so total work = 60 machine hours. Then \(12 * x = 60\), so \(x = 5\). But \(y\) is still unknown, so \(\frac{12 * x}{y}\) is not fixed. Not sufficient.
Answer: A
