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When the two painters work together and independently ?

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yaser36
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When the two painters work together and independently ? [#permalink] New post   09 Sep 2016, 08:43
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When working alone, painter W can paint a room in 2 hours, and working alone, painter X can paint the same room in z hours. When the two painters work together and independently, they can paint the room in 3/4 of an hour. What is the value of z?
A) 3/4
B) 1[1/5]
C) 1[2/5]
D) 1[3/4]
E) 2
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BrushMyQuant
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When the two painters work together and independently ? [#permalink] New post   Updated on: 29 Oct 2022, 10:48
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Rate*Time=Work

Let Painter W's rate be W and Painter X's rate be X
R*T = Work
W * 2 = 1 (If the work done is same throughout the question then the work done can be taken as 1) => W = 1/2
X * z = 1 => X = 1/z

When they both work together then their rates get added up
Combined Rate = (W+X)
R*T = Work
(W+X) * 3/4 = 1
=> W+X = 4/3
=> 1/2 + 1/z = 4/3
=> 1/z = (8-3)/6 = 5/6
=> z = 6/5 = 1[1/5]

So, Answer will be B
Hope it helps!

Watch the following video to learn How to Solve Work Rate Problems


Originally posted by BrushMyQuant on 09 Sep 2016, 08:53.
Last edited by BrushMyQuant on 29 Oct 2022, 10:48, edited 2 times in total.
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Re: When the two painters work together and independently ? [#permalink] New post   09 Sep 2016, 08:53
yaser36 wrote:
When working alone, painter W can paint a room in 2 hours, and working alone, painter X can paint the same room in z hours. When the two painters work together and independently, they can paint the room in 3/4 of an hour. What is the value of z?
A) 3/4
B) 1[1/5]
C) 1[2/5]
D) 1[3/4]
E) 2


The formula for work rate when 2 people work together is \(\frac{1}{3/4} = \frac{1}{z} + \frac{1}{2}\)
solve for z and it will be \(\frac{6}{5} or 1 \frac{1}{5}\)
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Re: When the two painters work together and independently ? [#permalink] New post   16 Mar 2017, 12:11
yaser36 wrote:
When working alone, painter W can paint a room in 2 hours, and working alone, painter X can paint the same room in z hours. When the two painters work together and independently, they can paint the room in 3/4 of an hour. What is the value of z?
A) 3/4
B) 1[1/5]
C) 1[2/5]
D) 1[3/4]
E) 2


While I originally solved these types of problems by guessing and plugging in values and trying to set the fractions equal to each other, I have now learned a much more efficient way of solving these problems thanks to others on the board.

Painter W= 1 job/ 2 hours

Painter Z= 1 job/ x hours

Painter W and Z combined work rate= 1 job / 3/4 hour

1/2 + 1/x = 1/(3/4)
1/x= 1/(3/4)-1/2
1/x=4/3-1/2
1/x=8/6-1/2
1/x=8/6-3/6
1/x=5/6
x=6/5
x=1 1/5
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Re: When the two painters work together and independently ? [#permalink] New post   17 Mar 2017, 01:42
yaser36 wrote:
When working alone, painter W can paint a room in 2 hours, and working alone, painter X can paint the same room in z hours. When the two painters work together and independently, they can paint the room in 3/4 of an hour. What is the value of z?
A) 3/4
B) 1[1/5]
C) 1[2/5]
D) 1[3/4]
E) 2

let the total work be T, rate of worker W and X be w and x respectively

2w = T, w = T/2
xz = T, x = T/z

(w+x)*3/4 = T

Replacing w and x, we get

(T/2 + T/z)*3/4 = T

cancelling T and solving for z, we get
z = 6/5 or 1 1/5
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Re: When the two painters work together and independently ? [#permalink] New post   21 Mar 2017, 06:20
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yaser36 wrote:
When working alone, painter W can paint a room in 2 hours, and working alone, painter X can paint the same room in z hours. When the two painters work together and independently, they can paint the room in 3/4 of an hour. What is the value of z?
A) 3/4
B) 1[1/5]
C) 1[2/5]
D) 1[3/4]
E) 2


We are given that painter W can paint a room in 2 hours and that painter X can paint the same room in z hours. Thus, the rate of painter W is 1/2 and the rate of painter X is 1/z. We are also given that when they work together they can paint the room in 3/4 of an hour. Thus, their combined rate is 1/(3/4) = 4/3. We can create the following equation and determine z:

1/2 + 1/z = 4/3

Multiplying the equation by 6z, we have:

3z + 6 = 8z

6 = 5z

z = 6/5 = 1 1/5

Answer: B
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When the two painters work together and independently ? [#permalink] New post   21 Mar 2017, 10:58
yaser36 wrote:
When working alone, painter W can paint a room in 2 hours, and working alone, painter X can paint the same room in z hours. When the two painters work together and independently, they can paint the room in 3/4 of an hour. What is the value of z?
A) 3/4
B) 1[1/5]
C) 1[2/5]
D) 1[3/4]
E) 2


combined rate=1/2+1/z=4/3
1/z=4/3-1/2=5/6
inverting, z=6/5=1 1/5 hours
B
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Re: When the two painters work together and independently ? [#permalink] New post   06 Jan 2024, 00:26
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Re: When the two painters work together and independently ? [#permalink]
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