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A factory has four assembly machines that operate at constan 19 Mar 2026, 06:40
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45% (medium)

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77% (02:52) correct 23% (02:55) wrong based on 118 sessions

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A toy factory has four assembly machines that operate at constant rates. Machine C takes 3 times as long as machine A to assemble a given number of items. Machine B takes 4 times as long as machine C and twice as long as machine D. How long would it take machine A alone to assemble the same number of items that machines B, C, and D working together can assemble in 1 hour?

A. 20 minutes
B. 35 minutes
C. 45 minutes
D. 51 minutes
E. 60 minutes
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B
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A factory has four assembly machines that operate at constan 20 Jun 2026, 10:29
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Here's my solution:
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errornisi
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A factory has four assembly machines that operate at constan 25 Jun 2026, 07:14
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Hi,

It says " Machine C takes 3 times as long as machine A" so doesn't that mean C= 1/3A or A=3C?
Thanks in advance.
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Bunuel
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A factory has four assembly machines that operate at constan 25 Jun 2026, 07:48
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A toy factory has four assembly machines that operate at constant rates. Machine C takes 3 times as long as machine A to assemble a given number of items. Machine B takes 4 times as long as machine C and twice as long as machine D. How long would it take machine A alone to assemble the same number of items that machines B, C, and D working together can assemble in 1 hour?

A. 20 minutes
B. 35 minutes
C. 45 minutes
D. 51 minutes
E. 60 minutes

Let machine A’s rate be 12 units per hour.

Then:

  • C takes 3 times as long as A, so C’s rate is 4 units per hour.
  • B takes 4 times as long as C, so B’s rate is 1 unit per hour.
  • B takes twice as long as D, so D is twice as fast as B. Thus D’s rate is 2 units per hour.

Together, B, C, and D assemble:

1 + 4 + 2 = 7 units per hour

Machine A assembles 12 units per hour, so the time A needs to assemble 7 units is:

7/12 hour = 35 minutes

Answer: B.

errornisi
Hi,

It says " Machine C takes 3 times as long as machine A" so doesn't that mean C= 1/3A or A=3C?
Thanks in advance.
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It depends on what A and C denote.

If A and C denote times, then C = 3A, because Machine C takes 3 times as long as Machine A.
If A and C denote rates, then C = A/3, because taking 3 times as long means working at one-third the rate.
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A factory has four assembly machines that operate at constan 27 Jun 2026, 14:30
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A = 3C
B = 1/4 (C)
D = 1/2 (C)

B + D + C = 1/4 + 1/2 + 1 = Rate of 7/4 combined.

7/4 / 3 = 7/12

7/12 * 60 = 35 minutes.
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