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A metal company's old machine makes bolts at a constant rate of 100

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A metal company's old machine makes bolts at a constant rate of 100  [#permalink]

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New post 14 Sep 2017, 04:03
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A metal company's old machine makes bolts at a constant rate of 100 bolts per hour.The company's new machine makes bolts at a constant rate of 150 bolts per hour. If both machines start at the same time and continue making bolts simultaneously, how many minutes will it take the two machines to make a total of 300 bolts?

A. 36
B. 72
C. 120
D. 144
E. 180

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Re: A metal company's old machine makes bolts at a constant rate of 100  [#permalink]

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New post 14 Sep 2017, 04:28
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Bunuel wrote:
A metal company's old machine makes bolts at a constant rate of 100 bolts per hour.The company's new machine makes bolts at a constant rate of 150 bolts per hour. If both machines start at the same time and continue making bolts simultaneously, how many minutes will it take the two machines to make a total of 300 bolts?

A. 36
B. 72
C. 120
D. 144
E. 180


First way: In an hour you will make: 100+150 = 250.

So in two -> 500 > 300.
Which means C,D,E falls immediately.
Also, everything under an hour, A falls.

-> and the answer is B. 72.

Second way:

12 minutes = 1/5 of an hour, so that's 150/5 + 100/5 = 30+20 = 50.
300 would need 6 times that.
So 12*5 = 72 minutes.
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Re: A metal company's old machine makes bolts at a constant rate of 100  [#permalink]

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New post 14 Sep 2017, 05:07
Bunuel wrote:
A metal company's old machine makes bolts at a constant rate of 100 bolts per hour.The company's new machine makes bolts at a constant rate of 150 bolts per hour. If both machines start at the same time and continue making bolts simultaneously, how many minutes will it take the two machines to make a total of 300 bolts?

A. 36
B. 72
C. 120
D. 144
E. 180

Total bolts in 1 hour of both machines: 250
So 300 bolts/250 bolts=6/5
60/5*6= 72 minutes
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Re: A metal company's old machine makes bolts at a constant rate of 100  [#permalink]

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New post 17 Sep 2017, 14:10
In one hour, they'll do 250 bolts. There are still 50 missing, and since they make 250 per hour, they'll need 50/250 * 60 (minutes) = 12 minutes to do the remaining 50 bolts.

Hence, B.
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Re: A metal company's old machine makes bolts at a constant rate of 100  [#permalink]

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New post 18 Sep 2017, 05:45
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1
Bunuel wrote:
A metal company's old machine makes bolts at a constant rate of 100 bolts per hour.The company's new machine makes bolts at a constant rate of 150 bolts per hour. If both machines start at the same time and continue making bolts simultaneously, how many minutes will it take the two machines to make a total of 300 bolts?

A. 36
B. 72
C. 120
D. 144
E. 180


We can let t = the time in hours the machines work together; thus:

100t + 150t = 300

250t = 300

t = 30/25 = 6/5 hours, which is 6/5 x 60 = 72 minutes.

Answer: B
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Re: A metal company's old machine makes bolts at a constant rate of 100  [#permalink]

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New post 17 Mar 2018, 12:36
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Hi All,

The answer choices to this question provide a fantastic shortcut. With the two machines that we're given, we know that...

Old Machine = 100 bolts/hour
New Machine = 150 bolts/hour

If they start at the same time, the two machines will create 250 bolts/hour

The question asks how long it would take the two machines to make 300 bolts, so we know it's going to be more than 1 hour.

If the two machines worked for 2 hours, then they'd make 500 bolts, but that's too many bolts.

We need an answer that's more than 1 hour, but less than 2 hours. The question also asks for an answer IN MINUTES. The ONLY answer that fits is the one that's between 60 minutes and 120 minutes.

Final Answer:

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Re: A metal company's old machine makes bolts at a constant rate of 100  [#permalink]

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New post 31 Jan 2019, 06:07
Bunuel wrote:
A metal company's old machine makes bolts at a constant rate of 100 bolts per hour.The company's new machine makes bolts at a constant rate of 150 bolts per hour. If both machines start at the same time and continue making bolts simultaneously, how many minutes will it take the two machines to make a total of 300 bolts?

A. 36
B. 72
C. 120
D. 144
E. 180

\(?\,\,\, = \,\,\,T\,\,\left[ {\min } \right]\)

Perfect opportunity for UNITS CONTROL, one of the most powerful tools carefully explained in our course!

\(300\,\,{\text{bolts}}\,\,\,\,{\text{ = }}\,\,\,\,\left( {\frac{{100\,\,{\text{bolts}}}}{{60\,\,\min }}} \right)\,\, \cdot \,\,T\,\,\min \,\,\, + \,\,\,\left( {\frac{{150\,\,{\text{bolts}}}}{{60\,\,\min }}} \right)\,\, \cdot \,\,T\,\,\min\)

\(300\,\,\, = \,\,\,\frac{{5 \cdot \boxed2}}{{3 \cdot \boxed2}}T\,\, + \,\,\frac{{5 \cdot \boxed3}}{{2 \cdot \boxed3}}T\,\,\, = \,\,\,\frac{{25}}{6}T\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,T = \frac{6}{{25}}300 = 6 \cdot 3 \cdot 4 = 72\)


The correct answer is therefore (B).


We follow the notations and rationale taught in the GMATH method.

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Re: A metal company's old machine makes bolts at a constant rate of 100  [#permalink]

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New post 31 Jan 2019, 08:01
Bunuel wrote:
A metal company's old machine makes bolts at a constant rate of 100 bolts per hour.The company's new machine makes bolts at a constant rate of 150 bolts per hour. If both machines start at the same time and continue making bolts simultaneously, how many minutes will it take the two machines to make a total of 300 bolts?

A. 36
B. 72
C. 120
D. 144
E. 180


Efficiency of Old Machine = 100
Efficiency of New Machine = 150

Thus, Efficiency of Old + New Machine = 250

So, The machine will produce 300 bolts in 1.xx Hours

1 Hour = 60 min , so the Answer must be a few minutes more than 60 min, Among the given options only (B) matches, Answer must be (B) 72
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Re: A metal company's old machine makes bolts at a constant rate of 100  [#permalink]

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New post 05 Feb 2019, 08:04
Bunuel wrote:
A metal company's old machine makes bolts at a constant rate of 100 bolts per hour.The company's new machine makes bolts at a constant rate of 150 bolts per hour. If both machines start at the same time and continue making bolts simultaneously, how many minutes will it take the two machines to make a total of 300 bolts?

A. 36
B. 72
C. 120
D. 144
E. 180


We can let t = the number of hours to produce 300 bolts and create the equation:

(100 + 150) x t = 300

t = 300/250 = 6/5 hours, which is 72 minutes.

Alternate Solution:

We note that the two machines working together will produce 100 + 150 = 250 bolts in 60 minutes. Also, we notice that in 120 minutes, the two machines will produce 250 x 2 = 500 bolts. Since 300 is between 250 and 500, the time necessary for the two machines to produce 300 bolts must be between 60 and 120 minutes; the only possible choice is 72 minutes.

Answer: B
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Re: A metal company's old machine makes bolts at a constant rate of 100   [#permalink] 05 Feb 2019, 08:04
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