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Two machines, Y and Z, work at constant rates producing identical item
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umg4147
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Two machines, Y and Z, work at constant rates producing identical item [#permalink] New post  Updated on: 16 May 2016, 10:51
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Two machines, Y and Z, work at constant rates producing identical items. Machine Y produces 3 items in the same time Machine Z produces 2 items. If machine Y takes 9 minutes to produce a batch of items, how many minutes does it take for machine Z to produce the same number of items?

A. 6
B. 9
C. 9 1/2
D. 12
E. 13 1/2
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Originally posted by umg4147 on 16 May 2016, 10:46.
Last edited by Bunuel on 16 May 2016, 10:51, edited 1 time in total.
Renamed the topic and edited the question.
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Bunuel
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Two machines, Y and Z, work at constant rates producing identical item [#permalink] New post  16 May 2016, 10:53
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umg4147 wrote:
Two machines, Y and Z, work at constant rates producing identical items. Machine Y produces 3 items in the same time Machine Z produces 2 items. If machine Y takes 9 minutes to produce a batch of items, how many minutes does it take for machine Z to produce the same number of items?

A. 6
B. 9
C. 9 1/2
D. 12
E. 13 1/2


Machine Z is 1.5 times slower than machine Y. So, if machine Y takes 9 minutes to produce a batch of items, then it takes machine Z 9*1.5 = 13.5 minutes to produce the same number of items.

Answer: E.
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Re: Two machines, Y and Z, work at constant rates producing identical item [#permalink] New post  14 Jun 2016, 12:35
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lf you assume that machine Y produces 3 items per minute then machine Z produces 2 items per minute. If machine Y takes 9 minutes to produce a batch of items, then machine Y produces 27 items in these 9 minutes. Since machine Z produces the same number of items, it should take machine Z 13.5 minutes to produce 27 items.

At times, it just helps to plug in numbers...
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Re: Two machines, Y and Z, work at constant rates producing identical item [#permalink] New post  16 May 2016, 12:36
Hey awsome bunuel, i went a bit long in deducing the actual relation between the Rates.

Now atleast i know what to think when i see such question and dont need to go on the practice pad .
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Two machines, Y and Z, work at constant rates producing identical item [#permalink] New post  14 Jun 2016, 14:16
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rate z/rate y=2/3
time z/time y=3/2
3/2*9=13 1/2 minutes
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Re: Two machines, Y and Z, work at constant rates producing identical item [#permalink] New post  28 Jul 2020, 02:23
umg4147 wrote:
Two machines, Y and Z, work at constant rates producing identical items. Machine Y produces 3 items in the same time Machine Z produces 2 items. If machine Y takes 9 minutes to produce a batch of items, how many minutes does it take for machine Z to produce the same number of items?

A. 6
B. 9
C. 9 1/2
D. 12
E. 13 1/2


Y- 3 items
Z- 2 items
Let the batch be of 27 items, therefore Y would take 1 min to produce 3 units and 9 mins to produce 27 items. (9 items taken is consistent with the time mentioned in the question for Y to produce the batch of items)
Time required by X to produce 27 items is 27/2 (as in 1 min X produces 2 units) = 13.5 mins or 13 1/2 mins.
E
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Two machines, Y and Z, work at constant rates producing identical item [#permalink] New post  27 Aug 2020, 08:28
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\(R_Y = \frac{3}{t}\)

\(R_Z = \frac{2}{t}\)

Establish t = 1

In 9 minutes:

Y produces \(\frac{3}{1} * 9 = 27\)

Z produces \(\frac{2}{t} * 9 = 18\)

\(27 - 18 = 9 \)

"How much time will Z need to produce other 9 items?"

\(\frac{9}{2} = 4.5 \)

Total time needed by Z = 9 + 4.5 = 13.5
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Re: Two machines, Y and Z, work at constant rates producing identical item [#permalink] New post  27 Aug 2020, 09:09
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Given

    • Two machines, Y and Z, work at constant rates producing identical items.
    • Machine Y produces 3 items at the same time Machine Z produces 2 items.
    • Machine Y takes 9 minutes to produce a batch of items.

To Find

    • Minutes it takes for machine Z to produce the same number of items.


Approach and Working Out

    • Speed ratio –
      o \(\frac{Y}{Z }\) = \(\frac{3}{2 }\)

    • Time ratio –
      o \(\frac{Y}{Z }\) = \(\frac{2}{3 }\)
    • Time for Y = 9 minutes.

    • Time for Z = \(\frac{3}{2 }\)× 9 minutes
      o = 13 ½ minutes

Correct Answer: Option E
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Re: Two machines, Y and Z, work at constant rates producing identical item [#permalink] New post  27 Aug 2020, 09:13
EgmatQuantExpert wrote:
Given

    • Two machines, Y and Z, work at constant rates producing identical items.
    • Machine Y produces 3 items at the same time Machine Z produces 2 items.
    • Machine Y takes 9 minutes to produce a batch of items.

To Find

    • Minutes it takes for machine Z to produce the same number of items.


Approach and Working Out

    • Speed ratio –
      o \(\frac{Y}{Z }\) = \(\frac{3}{2 }\)

    • Time ratio –
      o \(\frac{Y}{Z }\) = \(\frac{2}{3 }\)
    • Time for Y = 9 minutes.

    • Time for Z = \(\frac{3}{2 }\)× 9 minutes
      o = 13 ½ minutes

Correct Answer: Option E


Hi!
Great method.

Could you please explain it in further details?
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Re: Two machines, Y and Z, work at constant rates producing identical item [#permalink] New post  27 Aug 2020, 09:19
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Given: Two machines, Y and Z, work at constant rates producing identical items. Machine Y produces 3 items in the same time Machine Z produces 2 items.
Asked: If machine Y takes 9 minutes to produce a batch of items, how many minutes does it take for machine Z to produce the same number of items?

Machine Y takes time to produce a batch of items = 9 mins
Machine X will take time to produce a batch of items = 9*3/2 = 27/2 = 13 1/2

IMO E
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Re: Two machines, Y and Z, work at constant rates producing identical item [#permalink] New post  28 Jun 2022, 01:47
umg4147 wrote:
Two machines, Y and Z, work at constant rates producing identical items. Machine Y produces 3 items in the same time Machine Z produces 2 items. If machine Y takes 9 minutes to produce a batch of items, how many minutes does it take for machine Z to produce the same number of items?

A. 6
B. 9
C. 9 1/2
D. 12
E. 13 1/2


__ | rate | time | work |
Y)__ 1.5r___ 9____ 1
Z)___ r___ 13.5___ 1

Working behind the matrix table:
It is given that Y produces 3 items in the same time Z produces 2
=> The rate of Y is 1.5 times faster than that of Z

I've assumed the batch size as 1 for simplicity.
In the stem, we're given:
1.5r*9=1
=> r= 1/13.5

Plugging the value of r in (Z):
1/r = 13.5
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santhosh1797
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Re: Two machines, Y and Z, work at constant rates producing identical item [#permalink] New post  30 Aug 2022, 03:05
Use W= nRT formula

R1*T1 = R2*T2

3*9 = 2*T2

T2= 13.5
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nimaki
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Re: Two machines, Y and Z, work at constant rates producing identical item [#permalink] New post  31 Aug 2022, 02:59
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|W |R |T |
Y|27|3 |9 |
Z|27|2 |X |

T = W/R = 27/2
T = 13.5 Min
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Re: Two machines, Y and Z, work at constant rates producing identical item [#permalink]
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