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Machine A produces bolts at a uniform rate of 120 every 40

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Machine A produces bolts at a uniform rate of 120 every 40 [#permalink]

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Machine A produces bolts at a uniform rate of 120 every 40 seconds, and Machine B produces bolts at a uniform rate of 100 every 20 seconds. If the two machines run simultaneously, how many seconds will it take for them to produce a total of 200 bolts?

(A) 22
(B) 25
(C) 28
(D) 32
(E) 56
[Reveal] Spoiler: OA

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Re: Machine A produces bolts at a uniform rate of 120 every 40 [#permalink]

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New post 07 Dec 2012, 04:05
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Walkabout wrote:
Machine A produces bolts at a uniform rate of 120 every 40 seconds, and Machine B produces bolts at a uniform rate of 100 every 20 seconds. If the two machines run simultaneously, how many seconds will it take for them to produce a total of 200 bolts?

(A) 22
(B) 25
(C) 28
(D) 32
(E) 56


Machine A produces 120/40=3 bolts per second;
Machine B produces 100/20=5 bolts per second.

Running simultaneously, they produce 3+5=8 bolts per second, thus it will take them 200/8=25 seconds to produce 200 bolts.

Answer: B.
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Machine A produces bolts at a uniform rate of 120 [#permalink]

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New post 12 Nov 2013, 08:49
Machine A produces bolts at a uniform rate of 120 every 40 seconds, and Machine B produces bolts at a uniform rate of 100 every 20 seconds. If the two machines run simultaneously, how many seconds will it take for them to produce a total of 200 bolts?

(A) 22
(B) 25
(C) 28
(D) 32
(E) 56


why cant i do it this way:
take 1/time taken for each machine to produce 20 bolts: thats (1/60) for A plus (1/100) for B. Then I add them up and take the reciprocal to get total time taken. thats 37.45. so its 37.45 bolts every 20 secs. so that 106.8 seconds for 200 bolts.

whats wrong with what I did?

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Re: Machine A produces bolts at a uniform rate of 120 [#permalink]

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New post 12 Nov 2013, 09:06
Machine A produces 120 bolts every 40 seconds.
How many bolts does Machine A produce every second?
Machine A produces 120/40 = 3 bolts every second.

Machine B produces 100 bolts every 20 seconds.
How many bolts does Machine B produce every second?
Machine B produces 100/20 = 5 bolts every second.

Together, Machine A and Machine B produces 3+5 = 8 bolts every second.

8 bolts / 1 sec = 200 bolts / x sec

Cross multiply, and get 200 = 8x; so, 25 = x.
So it takes 25 seconds to produce 200 bolts, when Machine A and Machine B work together.




Quote:
why cant i do it this way:
take 1/time taken for each machine to produce 20 bolts: thats (1/60) for A plus (1/100) for B. Then I add them up and take the reciprocal to get total time taken. thats 37.45. so its 37.45 bolts every 20 secs. so that 106.8 seconds for 200 bolts.


Unfortunately, I'm having trouble following your logic. It looks like you try to find how much time it takes to produce 20 bolts, but then later try to figure out how many bolts are produced every 20 seconds?
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Re: Machine A produces bolts at a uniform rate of 120 [#permalink]

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New post 12 Nov 2013, 09:23
I apply the simple formula: 1/(time taken by machine A) + 1/(time taken by machine B) = 1/(total time taken by both machines, together. this is now the rate (together). to get total time taken, inverse it. but i see what i did. i started adding the total bolts, thinking thats the time. i see my error, thank you. but the formula mentioned above (in my post) is correct, right?

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Machine A produces bolts at a uniform rate of 120 every 40 [#permalink]

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New post 11 Sep 2014, 06:35
Walkabout wrote:
Machine A produces bolts at a uniform rate of 120 every 40 seconds, and Machine B produces bolts at a uniform rate of 100 every 20 seconds. If the two machines run simultaneously, how many seconds will it take for them to produce a total of 200 bolts?

(A) 22
(B) 25
(C) 28
(D) 32
(E) 56


Machine A .. 120 in 40 seconds then 3 /sec
machine B .. 100 in 20 seconds then 5/sec

in one sec both can produce 8.

so for 200 , 200/8 = 25

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Machine A produces bolts at a uniform rate of 120 every 40 [#permalink]

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New post 30 Sep 2014, 23:16
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Time required = \(\frac{200}{\frac{120}{40} + \frac{100}{20}} = \frac{200}{8} = 25\)

Answer = B
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Re: Machine A produces bolts at a uniform rate of 120 every 40 [#permalink]

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New post 12 Oct 2016, 11:55
Walkabout wrote:
Machine A produces bolts at a uniform rate of 120 every 40 seconds, and Machine B produces bolts at a uniform rate of 100 every 20 seconds. If the two machines run simultaneously, how many seconds will it take for them to produce a total of 200 bolts?

(A) 22
(B) 25
(C) 28
(D) 32
(E) 56


Efficiency of machine A = 3 bolts/sec
Efficiency of machine B = 5 bolts/sec

Combined efficiency of the 8 bolts/sec

So, Time required to produce 200 bolts will be \(\frac{200}{8}\) = 25 seconds...

Answer will be (B) 25

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Re: Machine A produces bolts at a uniform rate of 120 every 40 [#permalink]

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Walkabout wrote:
Machine A produces bolts at a uniform rate of 120 every 40 seconds, and Machine B produces bolts at a uniform rate of 100 every 20 seconds. If the two machines run simultaneously, how many seconds will it take for them to produce a total of 200 bolts?

(A) 22
(B) 25
(C) 28
(D) 32
(E) 56


We are given that machine A produces bolts at a uniform rate of 120 every 40 seconds. Thus, the rate of Machine A is 120/40 = 3 bolts/second.

We are also given that Machine B produces bolts at a uniform rate of 100 every 20 seconds. Thus, the rate of Machine B is 100/20 = 5 bolts/second.

We need to determine the time it will take to produce 200 bolts when the two machines run simultaneously.

To determine the time to produce 200 bolts, we can use the combined work formula:

Work by Machine A + Work by Machine B = 200 bolts (the total work completed).

Because both machines are working simultaneously, we can say that they both work together for t seconds. We now can express the individual work done by Machine A and by Machine B. We must remember that work = rate x time.

Work done by Machine A = 3t

Work done by Machine B = 5t

3t + 5t = 200

8t = 200

t = 200/8 = 25

Answer: B
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Re: Machine A produces bolts at a uniform rate of 120 every 40 [#permalink]

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Re: Machine A produces bolts at a uniform rate of 120 every 40   [#permalink] 17 Oct 2017, 02:36
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