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# Each of two generators produces energy at a constant rate, but the two

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Math Expert
Joined: 02 Sep 2009
Posts: 55228
Each of two generators produces energy at a constant rate, but the two  [#permalink]

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27 Nov 2018, 00:05
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Difficulty:

25% (medium)

Question Stats:

82% (01:50) correct 18% (02:22) wrong based on 55 sessions

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Each of two generators produces energy at a constant rate, but the two rates are different. One of the generators produces n units of energy in 4 hours, and the other generator produces the same amount of energy in half the time. What fraction of n units of energy will be produced by both generators if they work simultaneously for 40 minutes?

A. 3/8
B. 1/2
C. 5/8
D. 3/4
E. 7/8

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Joined: 31 May 2018
Posts: 10
Re: Each of two generators produces energy at a constant rate, but the two  [#permalink]

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27 Nov 2018, 03:34
imo - b - 1.5 hrs

total hrs = 100
a's speed - 100/4 = 25
b's speed - 100/2 - 50

total speed - 75/hr

in 40 mins - 2/3*75 = 50.

CEO
Joined: 18 Aug 2017
Posts: 3493
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: Each of two generators produces energy at a constant rate, but the two  [#permalink]

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27 Nov 2018, 08:51
Bunuel wrote:
Each of two generators produces energy at a constant rate, but the two rates are different. One of the generators produces n units of energy in 4 hours, and the other generator produces the same amount of energy in half the time. What fraction of n units of energy will be produced by both generators if they work simultaneously for 40 minutes?

A. 3/8
B. 1/2
C. 5/8
D. 3/4
E. 7/8

(n/4+n/2) * (40 /60)

3n/4*(2/3)
n/2 option B
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VP
Joined: 09 Mar 2016
Posts: 1284
Each of two generators produces energy at a constant rate, but the two  [#permalink]

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27 Nov 2018, 09:41
Bunuel wrote:
Each of two generators produces energy at a constant rate, but the two rates are different. One of the generators produces n units of energy in 4 hours, and the other generator produces the same amount of energy in half the time. What fraction of n units of energy will be produced by both generators if they work simultaneously for 40 minutes?

A. 3/8
B. 1/2
C. 5/8
D. 3/4
E. 7/8

i converted hours to minutes so 4 hours 240 minuts and 2 hours 120 minutes

$$\frac{n}{240}$$ +$$\frac{n}{120}$$ = $$\frac{1}{40}$$

$$\frac{3n}{240} = \frac{1}{40}$$ cross multiply

$$n = \frac{240}{120}$$

$$n = 120$$ hence half i.e ---> $$\frac{1}{2}$$

B

chetan2u is my solution correct ? please let me know
VP
Joined: 09 Mar 2016
Posts: 1284
Re: Each of two generators produces energy at a constant rate, but the two  [#permalink]

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27 Nov 2018, 09:45
Archit3110 wrote:
Bunuel wrote:
Each of two generators produces energy at a constant rate, but the two rates are different. One of the generators produces n units of energy in 4 hours, and the other generator produces the same amount of energy in half the time. What fraction of n units of energy will be produced by both generators if they work simultaneously for 40 minutes?

A. 3/8
B. 1/2
C. 5/8
D. 3/4
E. 7/8

(n/4+n/2) * (40 /60)

3n/4*(2/3)
n/2 option B

hello Archit3110 are you multiplying total work done by part of work done ?
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Joined: 18 Aug 2017
Posts: 3493
Location: India
Concentration: Sustainability, Marketing
GPA: 4
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Re: Each of two generators produces energy at a constant rate, but the two  [#permalink]

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27 Nov 2018, 09:50
1
dave13 wrote:
Archit3110 wrote:
Bunuel wrote:
Each of two generators produces energy at a constant rate, but the two rates are different. One of the generators produces n units of energy in 4 hours, and the other generator produces the same amount of energy in half the time. What fraction of n units of energy will be produced by both generators if they work simultaneously for 40 minutes?

A. 3/8
B. 1/2
C. 5/8
D. 3/4
E. 7/8

(n/4+n/2) * (40 /60)

3n/4*(2/3)
n/2 option B

hello Archit3110 are you multiplying total work done by part of work done ?

dave13

Actually I skipped a step or two and did straight the calculation.

rate of generator @ 4hours : n/4 & @ 2 hours : n/2
combined rate (n/4)+(n/2)
3n/4
so in 40 mins i.e 40/60: 2/3 hours it would produce 2/3 * 3n/4 i.e n/2 which means 1/2 of n ...

hope this helps
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Posts: 7684
Re: Each of two generators produces energy at a constant rate, but the two  [#permalink]

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27 Nov 2018, 22:14
1
dave13 wrote:
Bunuel wrote:
Each of two generators produces energy at a constant rate, but the two rates are different. One of the generators produces n units of energy in 4 hours, and the other generator produces the same amount of energy in half the time. What fraction of n units of energy will be produced by both generators if they work simultaneously for 40 minutes?

A. 3/8
B. 1/2
C. 5/8
D. 3/4
E. 7/8

i converted hours to minutes so 4 hours 240 minuts and 2 hours 120 minutes

$$\frac{n}{240}$$ +$$\frac{n}{120}$$ = $$\frac{1}{40}$$

$$\frac{3n}{240} = \frac{1}{40}$$ cross multiply

$$n = \frac{240}{120}$$

$$n = 120$$ hence half i.e ---> $$\frac{1}{2}$$

B

chetan2u is my solution correct ? please let me know

Hi dave13,
You are solution is correct uptil a point and required an extra term to make sense..
What does $$\frac{n}{240}$$ +$$\frac{n}{120}$$ mean. It means addition of per minute work of both generators.
This should be equal to x/40, if they are making X in 40 minutes when combined.
While $$\frac{1}{40}$$ means that both make 1 in 40 minutes..

So the equation would be $$\frac{n}{240}$$ +$$\frac{n}{120}$$ = $$\frac{x}{40}$$....
And x=n/2 so HALF of n...
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Re: Each of two generators produces energy at a constant rate, but the two   [#permalink] 27 Nov 2018, 22:14
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