Lindsay can paint 1/x of a certain room in one hour. If Lindsay and Jo

Question

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. \(\frac{1}{3x}\)

B. \(\frac{x}{(x-3)}\)

C. \(\frac{(x-1)}{3x}\)

D. \(\frac{x}{(x-1)}\)

E. \(\frac{(x-1)}{x}\)

A.  \frac{1}{3x}

B.  \frac{x}{(x-3)}

C.  \frac{(x-1)}{3x}

D.  \frac{x}{(x-1)}

E.  \frac{(x-1)}{x}

Bunuel · Accepted Answer

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.

Answer: C.

Narenn · Answer

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.

Back to your question..........

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.

ezhilkumarank · Answer

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.

shalu · Answer

bunuel u always hit the nail to the point.......very easy explanation....thanks

Mindreko · Answer

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.

shadowgun · Answer

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 )

Richard0715 · Answer

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?

Narenn · Answer

Have you checked Option C using x=2 ?

\frac{(x-1)}{3x}  ---------->  \frac{(2-1)}{3X2}  ---------->  \frac{1}{6}  ------> Same as Option A

blueseas · Answer

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

GMAT40 · Answer

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

madn800 · Answer

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

PareshGmat · Answer

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}

Bunuel · Answer

Similar question to practice: https://gmatclub.com/forum/lindsay-can-p ... 56880.html

UmairKhan15 · Answer

Best approach for me is to plug in #s.

Say x=2, so Lindsay paints 1/2 of the room in one hour. Use  D=RT  for each Lindsay, Joseph and for both. (D:Work, R:Rate, T:Time) Say D=6

Consider Lindsay only: Lindsay paints 1/2 of D=6, meaning 3. Her rate is then R(Lindsay)=3 if T=1.

Consider Lindsay and Joseph: D=RT, D=6 and T=1, R becomes 6. R here is combined i.e., R= R(Lindsay)+R(Joseph)
R(Joseph) = 3 since R(Lindsay)=3.

Consider Joseph only: D=RT, R=3 and T= 20 min or 1/3 hr
D becomes 1. In other words, Joseph has painted 1/6 of the room in 20 min or 1/3 hr. 1/6 is target value. Plugin x=2 in Answer choices to match the target, C works.

cavana · Answer

1) First, let's find Lindsay's rate:  r*1=\frac{1}{x}, r=\frac{1}{x} 
2) Now let's find Lindsay and Joseph's rate when working together: R*1=1; R=1
3) Joseph's rate is equal to Lindsay and Joseph's rate together - Lindsay's rate:  R-r=1-\frac{1}{x} 
4) Joseph's work in 20 minutes is equal to his rate (per hour) divided by 3.  (1-\frac{1}{x})/3=\frac{x-1}{x}*\frac{1}{3}=\frac{x-1}{3x}

gracie · Answer

let 1/j=J's rate
1/j=1-(1/x)
1/j*1/3=1/3-1/3x=(x-1)/3x
C

ScottTargetTestPrep · Answer

We are given that Lindsay's rate to paint a room is 1/x. We are also given that when she works with Joseph, they can paint the room in 1 hour. If we let total work = 1 and j = the number of hours it takes Joseph to paint the room by himself, then Joseph’s rate = 1/j. We can create the following equation and isolate j.

work of Lindsay + work of Joseph = 1

(1/x)(1) + (1/j)(1) = 1

1/x + 1/j = 1

Multiplying the entire equation by xj, we obtain:

j + x = xj

x = xj - j

x = j(x - 1)

x/(x-1) = j

Since j = x/(x-1) and 1/j = Joseph’s rate, Joseph’s rate in terms of x is (x - 1)/x.

Since 20 minutes = 1/3 of an hour, and since work = rate x time, Joseph can complete:

(1/3) = (x - 1)/(3x) of the job in 20 minutes.

Answer: C

generis · Answer

If the algebraic equation eludes you, pick an unusual number for  x . Rates are in   \frac{rooms}{hr}

Let  x = 6 
L's rate =  \frac{1}{x}=\frac{1}{6}

L and J's combined rate = 
 (\frac{1}{6}+\frac{1}{J})=\frac{1}{1}

J's rate :  \frac{1}{J}=(\frac{1}{1} - \frac{1}{6}) = \frac{5}{6}

Work competed  in 20 minutes =  \frac{1}{3}  hour?
  RT= W  
In 20 minutes, J completes
 (\frac{5}{6}*\frac{1}{3}) =\frac{5}{18}  of a room

Using x = 5, find the answer* that yields  \frac{5}{18}

A.  \frac{1}{3x}=\frac{1}{(3*6)}=\frac{1}{18}  - NO

B.  \frac{x}{(x-3)}=\frac{6}{(6-3}=\frac{6}{3}=2  - NO

C.  \frac{(x-1)}{3x}=\frac{(6-1)}{18}=\frac{5}{18}  - MATCH

D.  \frac{x}{(x-1)}=\frac{6}{(6-1)}=\frac{6}{5} - NO

E.  \frac{(x-1)}{x}=\frac{(6-1)}{6}=\frac{5}{6}  - NO

Answer C

*1) if your answer is a fraction, do not reduce it (your answer is based on an assigned value for x - don't depart from that value); and 2) with this method you have to check all the answer choices

Mirren1 · Answer

I don't think this is a good question since you can plug the number 2 in and you would get A or C as the answer.

Can someone comment their opinion on the question quality?

Lindsay can paint 1/x of a certain room in one hour. If Lindsay and Jo

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