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# Two identical machines have the ability to produce both nuts and bolts

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Manager
Joined: 21 Aug 2014
Posts: 138
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Two identical machines have the ability to produce both nuts and bolts  [#permalink]

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16 Jun 2015, 00:18
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Difficulty:

25% (medium)

Question Stats:

74% (01:44) correct 26% (01:51) wrong based on 464 sessions

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Two identical machines have the ability to produce both nuts and bolts. However, it takes 1 second to produce a bolt but 2 seconds to produce a nut. What is the fastest the two machines, working together, can produce 1,000 nuts and 1,000 bolts?

(A) 1,250 seconds
(B) 1,500 seconds
(C) 1,750 seconds
(D) 2,000 seconds
(E) 3,000 seconds

Please provide a detailed explanation on how to approach such twisted work/rate questions.

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Joined: 02 Sep 2009
Posts: 54371
Re: Two identical machines have the ability to produce both nuts and bolts  [#permalink]

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16 Jun 2015, 01:34
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Patronus wrote:
Two identical machines have the ability to produce both nuts and bolts. However, it takes 1 second to produce a bolt but 2 seconds to produce a nut. What is the fastest the two machines, working together, can produce 1,000 nuts and 1,000 bolts?

(A) 1,250 seconds
(B) 1,500 seconds
(C) 1,750 seconds
(D) 2,000 seconds
(E) 3,000 seconds

Please provide a detailed explanation on how to approach such twisted work/rate questions.

To minimize the amount of time, we should make both machines work all the time while producing 1,000 nuts and 1,000 bolts.

Two machines to produce 1,000 bolts will need (1,000*1)/2 = 500 seconds.
Two machines to produce 1,000 nuts will need (1,000*2)/2 = 1,000 seconds.

Total = 500 + 1,000 = 1,500.

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Two identical machines have the ability to produce both nuts and bolts  [#permalink]

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16 Jun 2015, 01:45
1
Bunuel wrote:
To minimize the amount of time, we should make both machines work all the time while producing 1,000 nuts and 1,000 bolts.

Two machines to produce 1,000 bolts will need (1,000*1)/2 = 500 seconds.
Two machines to produce 1,000 nuts will need (1,000*2)/2 = 1,000 seconds.

Total = 500 + 1,000 = 1,500.

Hi Bunuel - thankyou for the answer.

I used the Rate formula (R=$$\frac{1}{T}$$)
Rate of 1st machine = Rate of making 1 bolt + Rate of making 1 nut = 1 + $$\frac{1}{2}$$
Rate of 1st machine = Rate of 2nd machine
After this I got lost.

Please can you help how to approach using algebra?
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Re: Two identical machines have the ability to produce both nuts and bolts  [#permalink]

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16 Jun 2015, 01:48
3
Patronus wrote:
Bunuel wrote:
To minimize the amount of time, we should make both machines work all the time while producing 1,000 nuts and 1,000 bolts.

Two machines to produce 1,000 bolts will need (1,000*1)/2 = 500 seconds.
Two machines to produce 1,000 nuts will need (1,000*2)/2 = 1,000 seconds.

Total = 500 + 1,000 = 1,500.

Hi Bunuel - thankyou for the answer.

I used the Rate formula (R=\frac{1}{T})
Rate of 1st machine = Rate of making 1 bolt + Rate of making 1 nut = 1 + \frac{1}{2}
Rate of 1st machine = Rate of 2nd machine
After this I got lost.

Please can you help how to approach using algebra?

I wouldn't complicate:
1 machine needs 1,000*1 seconds to produce 1,000 bolts, so 2 need half of that, so 1,000/2 seconds.
1 machine needs 1,000*2 seconds to produce 1,000 nuts, so 2 need half of that, so 1,000*2/2 seconds.
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Re: Two identical machines have the ability to produce both nuts and bolts  [#permalink]

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25 Jun 2015, 07:44
Or we could find the time it would take for one machine to produce 1000 nuts and 1000 bolts and divide it by 2, as there would be 2 similar machines.

So, one machine would take:
1000 seconds for 1000 bolts and
2000 seconds for 1000 nuts. Together,
3000 seconds for 1000 nuts and 1000 bolts.

If another machine, working at the same rate, was to be added, it would take half that time.
So, 3000/2 = 1500 ANS B
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Re: Two identical machines have the ability to produce both nuts and bolts  [#permalink]

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16 Sep 2015, 14:03
Since you are asked to find the time for two identical machines to make 1000 x and 1000 y, you can simplify the question to to:

the time it takes one machine to make 500 x and 500 y

and that is just 500*1 + 500*2 = 1500
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Re: Two identical machines have the ability to produce both nuts and bolts  [#permalink]

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16 Sep 2015, 21:11
The easiest way to solve this question would be by solving for the time.
Since the rate of producing the bolts is same for both the machines,

We can safely assume that the time required to produce nuts and bolts will be halved.

To produce 1000 bolts, both machines will need 500 seconds
TO produce 1000 nuts, both machines will need 1000 seconds

Hence, the total time = 1500 seconds (Option B)
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Re: Two identical machines have the ability to produce both nuts and bolts  [#permalink]

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14 Dec 2016, 06:28
Now that they're working simultaneously, the output will double for the same amount of time.

So per machine: 1 bolt per second + 1 nut per 2 seconds
This becomes: 2 bolts per second + 2 nuts per 2 seconds (=1 nut per second)

Total time: 1000 bolts/2 bolts per second + 1000 nuts / 1 nut per second = 500 + 1,000 = 1,500.
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Posts: 9
Re: Two identical machines have the ability to produce both nuts and bolts  [#permalink]

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28 Feb 2017, 06:22
Patronus wrote:
Two identical machines have the ability to produce both nuts and bolts. However, it takes 1 second to produce a bolt but 2 seconds to produce a nut. What is the fastest the two machines, working together, can produce 1,000 nuts and 1,000 bolts?

(A) 1,250 seconds
(B) 1,500 seconds
(C) 1,750 seconds
(D) 2,000 seconds
(E) 3,000 seconds

Please provide a detailed explanation on how to approach such twisted work/rate questions.

u must mention that both machine together produces 1 bolt in a seconf and 1 nut in 2 seconds. my understanding is each machine produces 1 bolt in 1 sec and 1 nut in 2 secs and the answer is 1250 sec
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Re: Two identical machines have the ability to produce both nuts and bolts  [#permalink]

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02 Mar 2017, 17:38
Patronus wrote:
Two identical machines have the ability to produce both nuts and bolts. However, it takes 1 second to produce a bolt but 2 seconds to produce a nut. What is the fastest the two machines, working together, can produce 1,000 nuts and 1,000 bolts?

(A) 1,250 seconds
(B) 1,500 seconds
(C) 1,750 seconds
(D) 2,000 seconds
(E) 3,000 seconds

Since each bolt takes 1 second to produce, the time to produce 1,000 bolts = 1,000 x 1 = 1,000 seconds.

Since each nut takes 2 seconds to produce, the time to produce 1,000 nuts = 1,000 x 2 = 2,000 seconds.

If there is only one machine, it will take 1,000 + 2,000 = 3,000 seconds to produce 1,000 bolts and 1,000 nuts. However, since there are two machines and they are working simultaneously, it will take only half as much time to produce the bolts and nuts. Thus, it takes 1,500 seconds for the two machines to produce 1,000 bolts and 1,000 nuts.

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Re: Two identical machines have the ability to produce both nuts and bolts  [#permalink]

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20 Jul 2017, 02:11
Option:B
Time consumed:0:47
Bolt:1 second==1000*1=1000 second
Nuts=2 seconds==1000*2=2000 seconds
total time consumed=3000 seconds
**but here we have two machines which work on same speed so
3000/2=1500 seconds
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Re: Two identical machines have the ability to produce both nuts and bolts   [#permalink] 20 Jul 2017, 02:11
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