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# Lindsay can paint 1/x of a certain room in one hour

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Lindsay can paint 1/x of a certain room in one hour [#permalink]

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08 Aug 2010, 13:46
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Lindsay can paint 1/x of a certain room in one hour. If Lindsay and Joseph, working together at their respective rates, can paint the room in one hour, what fraction of the room can Joseph paint in 20 minutes?

A. 1/3x
B. x/(x-3)
C. (x-1)/3x
D. x/(x-1)
E. (x-1)/x
[Reveal] Spoiler: OA

Last edited by Bunuel on 31 Aug 2013, 05:35, edited 3 times in total.
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08 Aug 2010, 21:14
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Answer is C -- $$(x-1/3x)$$

Given details:

Rate at which L work --1/x
Rate at which L&J work -- x

Rate at which J alone works -- $$(x-1/x)$$

Rate at which J alone works in 20 min. -- $$(x-1/x) * (20/60) => (x-1/x)*(1/3)$$

On a side note, maybe this post needs to be moved to the Problem solving section.
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09 Aug 2010, 03:12
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Jinglander wrote:
Lindsay can pain 1/x of a room in an hour. Joe and Lindsey together can paint a the room in an hour. Using x what part of the room can Joseph paint in 20 min

A 1/3x
b X/(x-3)
c X-1/3x
d x/x-1
E: x-1/x

If Lindsay can paint $$\frac{1}{x}$$ of a room in 1 hour and together they pain the whole room in 1 hour then Joe can pain1 $$1-\frac{1}{x}=\frac{x-1}{x}$$ of a room in 1 hour --> in 20 minute or in $$\frac{1}{3}$$ of an hour Joe can paint $$\frac{x-1}{3x}$$ of a room.

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09 Aug 2010, 09:54
bunuel u always hit the nail to the point.......very easy explanation....thanks
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28 Oct 2011, 16:31
Just wondering,

if the job took say, 2.5 hours to complete, how would the answer change?

I understand your working though Bunuel, it's very clear.
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02 May 2013, 12:00
Mindreko wrote:
Just wondering,

if the job took say, 2.5 hours to complete, how would the answer change?

I understand your working though Bunuel, it's very clear.

If the job takes Joseph and Lindsay 2.5 hours together to complete.

and Lindsay take as regular 1/x hours to complete.

Then the rate at which Jospeh works would be = 1/2.5 - 1/x
= (x - 2.5) / (2.5x)

Hence, in 20 minutes

2.5 hours = 150 mins, so in 20 mins he would complete : 2 / 15 * (x - 2.5 ) / (2.5 x )
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Re: Lindsay can paint 1/x of a certain room in one hour [#permalink]

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08 May 2013, 17:17
if you use a smart number 2 for x, then A would be correct. I got this problem wrong two times so far in my studies and make the same mistake. Can someone explain why they would not think to use the number 2 as a smart number going into this problem?
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Re: Lindsay can paint 1/x of a certain room in one hour [#permalink]

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08 May 2013, 21:51
Richard0715 wrote:
if you use a smart number 2 for x, then A would be correct. I got this problem wrong two times so far in my studies and make the same mistake. Can someone explain why they would not think to use the number 2 as a smart number going into this problem?

Have you checked Option C using x=2 ?

$$\frac{(x-1)}{3x}$$ ----------> $$\frac{(2-1)}{3X2}$$ ----------> $$\frac{1}{6}$$ ------> Same as Option A
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Lindsay can paint 1/x of a certain room in one hour. If Lind [#permalink]

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04 Aug 2013, 09:07
Lindsay can paint 1/x of a certain room in one hour. If Lindsay and Joseph, working together at their respective rates, can paint the room in one hour, what fraction of the room can Joseph paint in 20 minutes?

A)1/3x

B)x/(x-3)

C)(x – 1)/3x

D)x/(x-1)

E)(x – 1)/x

I used substitution of values for the variable x, when x=2 i get an answer and when x=3 i get another answer! Please highlight my mistake.
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Re: A question in VICs [#permalink]

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04 Aug 2013, 11:21
Lindsay can paint 1/x of a certain room in one hour. If Lindsay and Joseph, working together at their respective rates, can paint the room in one hour, what fraction of the room can Joseph paint in 20 minutes?

A)1/3x

B)x/(x-3)

C)(x – 1)/3x

D)x/(x-1)

E)(x – 1)/x

I used substitution of values for the variable x, when x=2 i get an answer and when x=3 i get another answer! Please highlight my mistake.

Wrong forum, but here we go:

Let x=2:

Lindsay paints 1/2 room in 1 hour. You can use the RTD formula. R*1=1/2, then R=1/2.

Let Joseph's rate = 1/y, they say that combined they can paint the room in 1 hour, so:

(1/2+1/y)*1=1, solve for y. Y is = to 1/6.

1/6 become your target value. Insert 2 in each answer choices, you will see that it only works for C. I think you made a mistake as you were not sure what was your actual target value.
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Re: A question in VICs [#permalink]

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04 Aug 2013, 23:23
Hi jinkev,

When x=2 is put in option A, ans =1/(3*2)=1/6. Also when x=2 in option C, ans=(2-1)/(3*2)=1/6. So how should i proceed now. Should I try with some other value for x?
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Re: A question in VICs [#permalink]

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05 Aug 2013, 01:29
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Well, I am not a fond of trying values or of backsolving methods.

So I will present different method to solve this one - Percent Method.

First some theory.
When we say a person can finish the given task in X hours, we can also say that he can finish $$\frac{100}{X}%$$ task in one hour (Whole task always equals to 100%)
When we say another person can finish the same task in Y hours, we can also say that he can finish $$\frac{100}{Y}%$$ task in one hour.
Finally we can say that they can finish $$(\frac{100}{X} + \frac{100}{Y})%$$ task in one hour.

We will try this method in a simple question
Q :- A can finish certain work in 10 days. B can finish the same work in 20 days. In how many days can they finish the work working together?
A can finish certain work in 10 days ------> He can complete 10% of the work in a day
B can finish the same work in 20 days. -------> He can complete 5% of the work in a day
Working together they can complete (10+5)% work in a day.
Now that we know Total work always equals 100% and that they are finishing 15% work in a day working together, So we can say that they can complete the total work in $$\frac{100}{15}$$ (i.e. 6.66) days.

Lindsay can paint $$\frac{1}{X}$$ of a certain room in one hour. --------> This simply states that Lindsay can paint the room in X hours -----------> Lindsay can paint $$(\frac{100}{X})%$$ of the room in one hour

Lindsay and Joseph, working together at their respective rates, can paint the room in one hour --------> Working together they can paint the 100% of the room in one hour

Equation is ( Rate of Lindsay of one hour + Joseph Rate of of one hour) = Rate of Lindsay+Joseph of one hour

$$\frac{100}{X}$$ + Joseph Rate of of one hour = 100 -------> Joseph's Rate of one hour = $$100 - \frac{100}{X}$$ --------->

Joseph's Rate of one hour = $$\frac{100(X - 1)}{X}$$ --------> We can rephrase this as Joseph is completing $$\frac{(100(X-1))}{X}%$$ of 100% room in one hour ----------> In Fraction He is completing $$\frac{(100(X-1))}{100X}$$ in one hour ------> $$\frac{(X-1)}{X}$$

what fraction of the room can Joseph paint in 20 minutes? ------------> what fraction of the room can Joseph paint in $$\frac{1}{3}$$ hour? -------> $$\frac{1}{3} \frac{(x-1)}{x}$$ -----> $$\frac{(x-1)}{3x}$$

Option C

Hope that Helps.
PS :- This question is already discussed here lindsay-can-paint-1-x-of-a-certain-room-in-one-hour-98789.html#p761312
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Re: A question in VICs [#permalink]

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05 Aug 2013, 01:50
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Lindsay can paint 1/x of a certain room in one hour. If Lindsay and Joseph, working together at their respective rates, can paint the room in one hour, what fraction of the room can Joseph paint in 20 minutes?

A)1/3x

B)x/(x-3)

C)(x – 1)/3x

D)x/(x-1)

E)(x – 1)/x

I used substitution of values for the variable x, when x=2 i get an answer and when x=3 i get another answer! Please highlight my mistake.

LINDSAY ==> 1/X of room in 1 hr
LINDSAY + JOSEPH ==> FULL ROOM i.e 1 ROOM IN 1 HR
JOSEPH 1 HR WORK + LINDSAY 1 HR WORK = FULL ROOM PAINTING = 1
JOSEPH 1 HR WORK + 1/X = 1
JOSEPH 1 HR WORK = 1- 1/X = (X-1)X
THEREFORE JOSEPH WORK IN 20 MINUTES(1/3 OF HOUR) =$$(1/3)*((X-1)/X)$$ = $$(X-1)/3X$$

Hope this helps
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Re: A question in VICs [#permalink]

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05 Aug 2013, 18:12
Let Joseph rate of work in 1 hr be y
Given : Lindsay rate of work in 1 hr as 1/x

Together,

1/x + y = 1

So Joseph rate of work would be

y = 1 - 1/x ==> x-1/x

In 20 min(1/3 of an hour), it would be 1/3(x-1/x) ==> x-1/3x
Option C
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Re: Lindsay can paint 1/x of a certain room in one hour [#permalink]

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12 Aug 2013, 15:24
Jinglander wrote:
Lindsay can paint 1/x of a certain room in one hour. If Lindsay and Joseph, working together at their respective rates, can paint the room in one hour, what fraction of the room can Joseph paint in 20 minutes?

A. 1/3x
B. x/(x-3)
C. (x-1)/3x
D. x/(x-1)
E. (x-1)/x

..................
1/x + 1/j = 1/1
or, j = x/(x-1) hours
x/(x-1) hours = 1 part
or, 20/60 hours = (x-1)/3x part
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Re: Lindsay can paint 1/x of a certain room in one hour [#permalink]

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30 Aug 2013, 16:58
1/x th of work-----1 hr
1 full work----------? hr --------x hrs by L to complete full work

Now xy/x+y=1
we have to find y i.e., hrs taken by J to complete full work

divide numerator and denominator of L.H.S with y
we get x divided by (x+y)*1/y=1
----x=(x+y)*1/y
----x=x/y+1
----x-1=x/y
----x-1/x=1/y
reciprocal both sides
----x/x-1=y

Now it takes x/x-1 hrs to complete 1 full work by J

then in 1/3 hrs i.e., 20 min----- ? work J completes

=1/3*1 whole divided by (x/x-1)
=1/3*(x-1/x)
=x-1/3x
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Solving equation question Manhatten GMAT cat test [#permalink]

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10 Dec 2014, 02:34
Hi all,

I have a problem to understand the explanation (in red) as given by the Manhatten GMAT test; question (Q) is as follows and explanation (E):

Q: Lindsay can paint 1/x of a certain room in one hour. If Lindsay and Joseph, working together at their respective rates, can paint the room in one hour, what fraction of the room can Joseph paint in 20 minutes?

E:

The work Lindsay does + the work Joseph does = the total work done. Let's say that the work Joseph does is 1/y.

Then we have this equation: 1/x + 1/y = 1

Solving for 1/y, we get 1/y = 1 - 1/x. The right-hand side of the equation simplifies to the following expression:

x – 1/x

So, how to come from 1/y= 1-1/x to x-1/x??

Hope to hear from you guys,

Kind regards,

Mathijs
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Solving equation question Manhatten GMAT cat test [#permalink]

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10 Dec 2014, 02:37
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Rate of Lindsay $$= \frac{1}{60x}$$

Rate of Joseph $$= \frac{1}{60} - \frac{1}{60x} = \frac{x-1}{60x}$$

Work done by Joseph in 20 Minutes $$= \frac{x-1}{60x} * 20 = \frac{x-1}{3x}$$
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Last edited by PareshGmat on 10 Dec 2014, 02:48, edited 1 time in total.
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Re: Solving equation question Manhatten GMAT cat test [#permalink]

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10 Dec 2014, 02:45
Mathijs wrote:
Hi all,

I have a problem to understand the explanation (in red) as given by the Manhatten GMAT test; question (Q) is as follows and explanation (E):

Q: Lindsay can paint 1/x of a certain room in one hour. If Lindsay and Joseph, working together at their respective rates, can paint the room in one hour, what fraction of the room can Joseph paint in 20 minutes?

E:

The work Lindsay does + the work Joseph does = the total work done. Let's say that the work Joseph does is 1/y.

Then we have this equation: 1/x + 1/y = 1

Solving for 1/y, we get 1/y = 1 - 1/x. The right-hand side of the equation simplifies to the following expression:

x – 1/x

So, how to come from 1/y= 1-1/x to x-1/x??

Hope to hear from you guys,

Kind regards,

Mathijs

This problem is posted complete at the link below:

lindsay-can-paint-1-x-of-a-certain-room-in-one-hour-98789.html

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Re: Lindsay can paint 1/x of a certain room in one hour [#permalink]

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10 Dec 2014, 04:06
Mathijs wrote:
Hi all,

I have a problem to understand the explanation (in red) as given by the Manhatten GMAT test; question (Q) is as follows and explanation (E):

Q: Lindsay can paint 1/x of a certain room in one hour. If Lindsay and Joseph, working together at their respective rates, can paint the room in one hour, what fraction of the room can Joseph paint in 20 minutes?

E:

The work Lindsay does + the work Joseph does = the total work done. Let's say that the work Joseph does is 1/y.

Then we have this equation: 1/x + 1/y = 1

Solving for 1/y, we get 1/y = 1 - 1/x. The right-hand side of the equation simplifies to the following expression:

x – 1/x

So, how to come from 1/y= 1-1/x to x-1/x??

Hope to hear from you guys,

Kind regards,

Mathijs

Merging topics. Please refer to the discussion above and ask if anything is still unclear.

Similar question to practice: lindsay-can-paint-1-x-of-a-certain-room-in-20-minutes-what-156880.html

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Re: Lindsay can paint 1/x of a certain room in one hour   [#permalink] 10 Dec 2014, 04:06

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