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# A painting crew painted 80 houses. They painted the first y houses at

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Math Expert
Joined: 02 Sep 2009
Posts: 50007
A painting crew painted 80 houses. They painted the first y houses at  [#permalink]

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09 Jun 2015, 02:56
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Difficulty:

55% (hard)

Question Stats:

69% (02:40) correct 31% (03:00) wrong based on 251 sessions

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A painting crew painted 80 houses. They painted the first y houses at a rate of x houses per week. Then more painters arrived and everyone worked together to paint the remaining houses at a rate of 1.25x houses per week. How many weeks did it take to paint all 80 houses, in terms of x and y?

A. (320 - y)/(5x)
B. (y +320)/(5x)
C. 5(80 - y)/(4x)
D. (y + 400)/(4x)
E. (4y + 320)/(5x)

Kudos for a correct solution.

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Posts: 6967
Re: A painting crew painted 80 houses. They painted the first y houses at  [#permalink]

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09 Jun 2015, 03:20
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1
Bunuel wrote:
A painting crew painted 80 houses. They painted the first y houses at a rate of x houses per week. Then more painters arrived and everyone worked together to paint the remaining houses at a rate of 1.25x houses per week. How many weeks did it take to paint all 80 houses, in terms of x and y?

A. (320 - y)/(5x)
B. (y +320)/(5x)
C. 5(80 - y)/(4x)
D. (y + 400)/(4x)
E. (4y + 320)/(5x)

Kudos for a correct solution.

total weeks= $$\frac{y}{x}$$ +$$\frac{(80-y)}{1.25x}$$ ...
=$$\frac{(y +320)}{(5x)}$$
ans B
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##### General Discussion
Manager
Joined: 12 Mar 2015
Posts: 92
GPA: 3.9
WE: Information Technology (Computer Software)
Re: A painting crew painted 80 houses. They painted the first y houses at  [#permalink]

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09 Jun 2015, 13:16
1
Let w1 and w2 be number of weeks.
So
First Week= x * w1 =y

Second Week = 5/4x * w2 = 80-y (Remaining houses)

Question is to find w1 + w2

i.e y/x + 80-y / 5/4x

= y+320/5x
= B
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Joined: 29 Mar 2015
Posts: 44
Location: United States
Re: A painting crew painted 80 houses. They painted the first y houses at  [#permalink]

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10 Jun 2015, 01:32
2
Another way to do this quickly is to plug in sets of easy numbers, such as $$Y=20, x=4$$ -> the first 20 take 5 weeks, and the second 60 at 5 houses per week take 12 so it totally takes 17 weeks.
In the answer choices, the denominator is either $$5x=20$$ or $$4x=16$$ so we want the numerator to be either 340 or 272
A: $$\frac{320-20}{20}=\frac{300}{20}$$ not 17.
B: $$\frac{20+320}{20}=\frac{340}{20}$$ is 17.
C: $$\frac{5*(80-20)}{16}=\frac{200}{16}$$ not 17.
D: $$\frac{400+20}{16}=\frac{420}{16}$$ not 17.
E: $$\frac{80-320}{20}=\frac{400}{20}$$ not 17.

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Re: A painting crew painted 80 houses. They painted the first y houses at  [#permalink]

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10 Jun 2015, 10:45
1
Total weeks= y/x +(80−y)/1.25x ...
=(y+320)/(5x)
Current Student
Joined: 02 Jun 2015
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Location: Brazil
Concentration: Entrepreneurship, General Management
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Re: A painting crew painted 80 houses. They painted the first y houses at  [#permalink]

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10 Jun 2015, 19:23
2
first part:
y houses at a x houses per week = y/x

second part:
rest of the houses at a 1.25x houses per week = 80-y / 1.25x

calculation:
y/x + 80-y/1.25x (multiple by 4 to make it easy)
4y/4x + 320 - 4y/5x
20y + 1280 - 16y / 20x
4y + 1280 / 20x (divide by 4 again)
y + 320 / 5x

Kudos if you like it
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Re: A painting crew painted 80 houses. They painted the first y houses at  [#permalink]

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12 Jun 2015, 19:03
1
y/x + (80-y)/1.25 --> Work together

Solve above equation gives

(y/4 + 80)/(5/4)x=y+320/5x. Ans is B
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Re: A painting crew painted 80 houses. They painted the first y houses at  [#permalink]

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13 Jun 2015, 10:20
1
Bunuel wrote:
A painting crew painted 80 houses. They painted the first y houses at a rate of x houses per week. Then more painters arrived and everyone worked together to paint the remaining houses at a rate of 1.25x houses per week. How many weeks did it take to paint all 80 houses, in terms of x and y?

A. (320 - y)/(5x)
B. (y +320)/(5x)
C. 5(80 - y)/(4x)
D. (y + 400)/(4x)
E. (4y + 320)/(5x)

Kudos for a correct solution.

Painted first y houses @x houses per week
To paint 1 house, time taken=1/x weeks
Therefore, to paint y houses, time taken=y/x weeks
Similarly, time taken to paint 80-y houses=80-y/1.25x
Total time taken=y/x+80-y/1.2x=4(0.25y+80)/5x=y+320/5x
Math Expert
Joined: 02 Sep 2009
Posts: 50007
Re: A painting crew painted 80 houses. They painted the first y houses at  [#permalink]

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15 Jun 2015, 03:12
Bunuel wrote:
A painting crew painted 80 houses. They painted the first y houses at a rate of x houses per week. Then more painters arrived and everyone worked together to paint the remaining houses at a rate of 1.25x houses per week. How many weeks did it take to paint all 80 houses, in terms of x and y?

A. (320 - y)/(5x)
B. (y +320)/(5x)
C. 5(80 - y)/(4x)
D. (y + 400)/(4x)
E. (4y + 320)/(5x)

Kudos for a correct solution.

MANHATTAN GMAT OFFICIAL SOLUTION:

This is a combined work problem, so we will use the work formula: rate × time = work. The work and rates are given, but we need to calculate time, so we manipulate the formula: time = work/rate. This is also a Variable In the answer Choices (VIC) problem, so it is efficient to pick numbers and test the answer choices.

We are told that there are 80 houses, that y houses are painted at a rate of x houses per week, and that the rate increases to 1.25x houses per week for the remaining 80 – y houses. We will pick values such that x and 1.25x are integers (i.e., x is a multiple of 4) and y and 80 – y are divisible by x and 1.25x, respectively.
Attachment:

2015-06-15_1409.png [ 52.77 KiB | Viewed 2849 times ]

The total painting time is:
20 houses painted at a rate of houses/week = 5 weeks
60 houses painted at a rate of 5 houses/week = 12 weeks
Total time for 80 houses = 5 + 12 = 17 weeks
Attachment:

2015-06-15_1412.png [ 45.33 KiB | Viewed 2845 times ]

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A painting crew painted 80 houses. They painted the first y houses at  [#permalink]

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10 Aug 2016, 05:34
Ans B
Plug some numbers
Let y = 40 houses and x = 20
then they painted 20 houses per week
as painters were added to the group , the rate of the group increased to 1.25 x => 1.25 * 20 = 25 houses per week

total time they took = (40/20) + (40/25) = 3.6 weeks

Putting the values of x and y in equation B

(y +320)/(5x) = (40+320)/5*20 = 360/100 = 3.6
Manager
Joined: 06 Oct 2015
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GMAT 1: 740 Q50 V40
Re: A painting crew painted 80 houses. They painted the first y houses at  [#permalink]

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10 Aug 2016, 07:23
Plug x=4 and y=40. Then It took 10 weeks to paint the first 40 houses.
Now the new working rate is 1.5*4=5 houes per week. So it takes 8 weeks to paint the remaining 40 houses.
Total 10+8=18 weeks.

Now plug the values in the answer choices and see only B gives 18.
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Re: A painting crew painted 80 houses. They painted the first y houses at  [#permalink]

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12 May 2018, 02:25
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