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Working alone, Manuel finishes cleaning half the house in a third of

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Working alone, Manuel finishes cleaning half the house in a third of  [#permalink]

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New post 12 Oct 2015, 22:20
2
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A
B
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D
E

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Working alone, Manuel finishes cleaning half the house in a third of the time it takes Nick to clean the entire house alone. Manuel alone cleans the entire house in 6 hours. How many hours will it take Nick and Manuel to clean the entire house if they work together?

A. 1.5
B. 2
C. 2.4
D. 3
E. 3.6

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Re: Working alone, Manuel finishes cleaning half the house in a third of  [#permalink]

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New post 12 Oct 2015, 22:40
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Working alone, Manuel finishes cleaning half the house in a third of the time it takes Nick to clean the entire house alone.

Manuel alone cleans the entire house in 6 hours.=>Manuel alone cleans the HALF OF entire house in 3 hours,WHICH IS
in a third of the time it takes Nick to clean the entire house alone.

SO,3 = 1/3 *time it takes Nick to clean the entire house alone
So,Nick takes 9 hours.
So,together,they in 1 hour they will do 1/9 + 1/6. Ans-3.6 hrs
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Re: Working alone, Manuel finishes cleaning half the house in a third of  [#permalink]

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New post 12 Oct 2015, 23:11
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Bunuel wrote:
Working alone, Manuel finishes cleaning half the house in a third of the time it takes Nick to clean the entire house alone. Manuel alone cleans the entire house in 6 hours. How many hours will it take Nick and Manuel to clean the entire house if they work together?

A. 1.5
B. 2
C. 2.4
D. 3
E. 3.6

Kudos for a correct solution.


Manuel finishes cleaning half the house in a third of the time it takes Nick to clean the entire house alone

i.e. Manuel finishes cleaning FULL house in TWO third of the time it takes Nick to clean the entire house alone

i.e. M = (3/2)N where M and N are efficiencies of Manuel and Nick

Time taken by M to clean House = 6 hours
i.e. Time taken by N to clean House = (3/2)*6 = 9 hours

1 Hour work of both M and N working together = (1/6)+(1/9) = (3+2)/18 = 5/18

5/18 House is cleaned by them together in 1 hours
Full House will be cleaned by them together in 1/(5/18) = 18/5 = 3.6 hours

Answer: option E
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Re: Working alone, Manuel finishes cleaning half the house in a third of  [#permalink]

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New post 13 Oct 2015, 05:36
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Answer is 3.6 hours.

Manuel does the complete house in 6 hours while Nick does it in 9 hours. 1/ (1/6+1/9)= 3.6
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Re: Working alone, Manuel finishes cleaning half the house in a third of  [#permalink]

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New post 13 Oct 2015, 06:10
Bunuel wrote:
Working alone, Manuel finishes cleaning half the house in a third of the time it takes Nick to clean the entire house alone. Manuel alone cleans the entire house in 6 hours. How many hours will it take Nick and Manuel to clean the entire house if they work together?

A. 1.5
B. 2
C. 2.4
D. 3
E. 3.6

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Manuel needs 6 Hours to complete the job
Nich needs 9 Hours to complete the job
-->t*(1/6+1/9)=1 --> t=18/5=3,6 Answer (E)
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Re: Working alone, Manuel finishes cleaning half the house in a third of  [#permalink]

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New post 15 Oct 2015, 01:31
Answer: E

1) Nike's time to clean the house is t, Manuel's time to clean 1/2 of the house is 1/3*t.

2) Manuel cleans 1/2 of the house is 3 hours (1/2*6 hours)

3) Nike's time t=1/3*3 = 9 hours

4) Manuel's rate (r1) - 1/6 house/hour; Nike's rate (r2) - 1/9 house/hour. r1+r2 = 1/6 + 1/9 = 5/18.

5) Time to clean the entire house for Nick and Manuel is 18/5 hours = 3.6 hours.
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Re: Working alone, Manuel finishes cleaning half the house in a third of  [#permalink]

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New post 06 May 2016, 13:48
If Manuel cleans the entire house alone in 6 hrs, then he cleans half the house in 3 hrs
But we know that this is 1/3rd the time required by Nick to clean the entire house alone
so Nick requires 9 hrs to clean the the entire house alone
combined rate when both Manuel and Nick work together is
\(\frac{1}{6}\)+ \(\frac{1}{9}\) = \(\frac{5}{18}\)

Time required = \(\frac{18}{5}\) = 3.6 hrs

correct answer - E
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Re: Working alone, Manuel finishes cleaning half the house in a third of  [#permalink]

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New post 06 May 2016, 14:26
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This question is easier than most because if Manuel and and Nick both cleaned the house at the same rate (6 hours / house) they would clean one house together in 3 hours, but since Nick is slower than Manuel, you know very quickly that the answer is > 3, and the only option greater than 3 is 3.6 (E).
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Re: Working alone, Manuel finishes cleaning half the house in a third of  [#permalink]

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New post 15 May 2018, 05:44
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Bunuel wrote:
Working alone, Manuel finishes cleaning half the house in a third of the time it takes Nick to clean the entire house alone. Manuel alone cleans the entire house in 6 hours. How many hours will it take Nick and Manuel to clean the entire house if they work together?

A. 1.5
B. 2
C. 2.4
D. 3
E. 3.6

Kudos for a correct solution.


Another option for many work questions is to assign a nice value to the given job.
Here, a nice value will be one that works well with the given numbers (6 hours, 1/2 the time, 1/3 of the time)
So, have about 36.
Let's say the entire job of cleaning the house consists of cleaning 36 rooms.

Manuel alone cleans the ENTIRE house in 6 hours.
So, Manuel can clean 36 rooms in 6 hours
So, Manuel's RATE = 6 rooms per HOUR

Working alone, Manuel finishes cleaning half the house in a third of the time it takes Nick to clean the entire house alone.
Half the house = 18 rooms
Since Manuel's RATE is 6 rooms per hour, Manuel can clean 18 rooms in 3 hours
We're told that this cleaning time is 1/3 of the time it takes Nick to clean the ENTIRE house alone
So, it must take Nick 9 hours to clean the ENTIRE house alone
The ENTIRE house consists of cleaning 36 rooms.
Rate = output/time
So, Nick's rate = 36/9 = 4 rooms per hour

How many hours will it take Nick and Manuel to clean the entire house if they work TOGETHER?
Manuel's RATE = 6 rooms per hour
Nick's rate = 4 rooms per hour
So, their COMBINED rate = 6 + 4 = 10 rooms per hour

time = output/rate
So, time = 36/10 = 3.6 hours

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Re: Working alone, Manuel finishes cleaning half the house in a third of  [#permalink]

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New post 16 May 2018, 10:42
Bunuel wrote:
Working alone, Manuel finishes cleaning half the house in a third of the time it takes Nick to clean the entire house alone. Manuel alone cleans the entire house in 6 hours. How many hours will it take Nick and Manuel to clean the entire house if they work together?

A. 1.5
B. 2
C. 2.4
D. 3
E. 3.6


We see that Manuel’s rate is 1/6, so it takes him 3 hours to clean half the house. This means it will take Nick 9 hours to clean the entire house. Thus, Nick’s rate is 1/9.

Working together, their combined rate is 1/6 + 1/9 = 3/18 + 2/18 = 5/18, so the time it takes them to clean the entire house is 1/(5/18) = 18/5 = 3.6 hours.

Answer: E
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Re: Working alone, Manuel finishes cleaning half the house in a third of  [#permalink]

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New post 19 May 2018, 06:15
Bunuel wrote:
Working alone, Manuel finishes cleaning half the house in a third of the time it takes Nick to clean the entire house alone. Manuel alone cleans the entire house in 6 hours. How many hours will it take Nick and Manuel to clean the entire house if they work together?

A. 1.5
B. 2
C. 2.4
D. 3
E. 3.6

Kudos for a correct solution.


Manuel can finish half the house in 1/3 of the time Nick takes
Implies Manuel can complete full house i.e 1/2 x 2 in 1/3 x 2 = 2/3 of the time taken by nick

Nick hourly rate is 1/6
Manuel rate = 2/3 of 1/6 = 1/9
Together 1/6 + 1/9 = 15/54

Or time taken 54/15 = 3.6 hours
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Re: Working alone, Manuel finishes cleaning half the house in a third of  [#permalink]

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New post 08 Oct 2018, 15:36
I can rewrite as the following:

1/3:1/2=6:x since Manuel alone cleans the entire house in 6 hours"
So, x=9.
When they work together, it can be expressed as the following rates:
1/6+1/3=1/h
or (9+6)/54=15/54=1/h
h=54/15=3.6
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Re: Working alone, Manuel finishes cleaning half the house in a third of   [#permalink] 08 Oct 2018, 15:36
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