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

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

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New post 09 Jun 2015, 02:56
1
1
5
00:00
A
B
C
D
E

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Question Stats:

72% (01:46) correct 28% (02:16) wrong based on 244 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)

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

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New post 09 Jun 2015, 03:20
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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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Re: A painting crew painted 80 houses. They painted the first y houses at  [#permalink]

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

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New post 10 Jun 2015, 01:32
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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.

So the answer 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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New post 10 Jun 2015, 10:45
1
IMO answer is B
Total weeks= y/x +(80−y)/1.25x ...
=(y+320)/(5x)
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Re: A painting crew painted 80 houses. They painted the first y houses at  [#permalink]

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New post 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

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

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New post 12 Jun 2015, 19:03
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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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New post 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
Answer B
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Re: A painting crew painted 80 houses. They painted the first y houses at  [#permalink]

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New post 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
2015-06-15_1409.png [ 52.77 KiB | Viewed 2721 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
2015-06-15_1412.png [ 45.33 KiB | Viewed 2717 times ]

The correct answer is B.
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PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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

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

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New post 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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