Lindsay can paint 1/x of a certain room in 20 minutes. What fraction

Question

Lindsay can paint 1/x of a certain room in 20 minutes. What fraction of the same room can Joseph paint in 20 minutes if the two of them can paint the room in an hour, working together at their respective rates?

A) 1/3x
B) 3x/(x – 3)
C) (x – 3)/3x
D) x/(x – 3)
E) (x – 3)/x

A.  \frac{1}{3x}

B.  \frac{3x}{(x – 3)}

C.  \frac{(x – 3)}{3x}

D.  \frac{x}{(x – 3)}

E.  \frac{(x – 3)}{x}

Bunuel · Accepted Answer

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

Answer: C.

zishu912 · Answer

Let's assume that total unit of work is 1 unit
Since Lindsay paints 1/x of certain paint in 20 minutes; therefore, the efficiency of Lindsay is 1/20x
and together they complete the 1 unit of work in 60 minutes, therefore their combined efficiency is 1/60

eff(Lindsay)+eff(joseph)=1/60
i/20x + eff(joseph) = 1/60
eff(joseph) = 1/60 - 1/20x =(x-3)/60x

so joseph will complete the work in 60x/(x-3) minutes

so in 20 minutes he will complete (x-3)/60x * 20 units of work = (x-3)/3x

Hremehre · Answer

Great approach by bunuel.

It is also an option to plug in numbers.
If x=3 then Lindsay paints 1/3 in 20 minutes = 3/3 in 1 hour, i.e. she paints the entire room herself. Therefore x=3 should make Joseph = 0.
C and E achieves this goal
C: 3-3/3*3 = 0/9 = 0
E: 3-3/3 = 0/3 = 0

x=6 means Lindsay paints 1/6 room per 20 minuters = 3/6 = 1/2 room in 1 hour. Therefore x=6 should make Joseph paint 1/2 in 1 hour, i.e. 1/6 in 20 minutes (same work rate as Lindsay actually).
C: (6-3)/(3*6) = 3/18 = 1/6 correct
E: (6-3)/6 = 3/6 NOT correct

Answer is C.

KarishmaB · Answer

Since rate of Lindsay is not given, you can assume a rate. Of course, if we are going to assume, we will assume the simplest case - both have same rate.
Both working together, take 1 hour to paint. Say, their rates are same and they both take 2 hrs each when working individually. 
Since in 120 mins, Lindsay paints 1 room, she paints 1/6th (x = 6) of the room in 20 mins. So Joseph should also paint 1/6th of the room in 20 mins.
So, if x = 6, the correct option should give us 1/6.

Only (C) does that.

Bowtye · Answer

What a great question! I got so caught up solving for the portion that Joseph completed in the hour that I completely forgot to multiply by 1/3 at the end to actually answer the question. In an effort to complete the question fast, I picked E. If I read the question one more time after doing the math, I would have gotten it correct. Lesson learned! Thank you for sharing.

JeffTargetTestPrep · Answer

We are given that Lindsay can paint 1/x of a room in 20 minutes; thus, she can paint 3/x of a room in 60 minutes (or in 1 hour). Thus, her hourly rate is 3/x room/hr. We are also given that when she works with Joseph, they can paint the entire 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 room/hr. We can create the following equation and isolate j:

work of Lindsay + work of Joseph = 1

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

3/x + 1/j = 1

Multiplying the entire equation by xj, we obtain:

3j + x = xj

x = xj - 3j

x = j(x - 3)

x/(x - 3) = j

Since j = x/(x - 3) and 1/j = Joseph’s rate, then Joseph’s rate, in terms of x, is (x - 3)/x.

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

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

Alternate Solution:

Since Lindsay and Joseph, working together, can paint the whole room in 1 hour, then in 20 minutes, they can paint 1/3 of the room. If we let r be the fraction of the room that Joseph can paint in 20 minutes, then it must be true that:

1/x + r = 1/3

r = 1/3 - 1/x

Using a common denominator of (3x), we obtain:

r = (x - 3)/(3x)

Answer: C

101mba101 · Answer

Hi Bunuel,

Can you explain how you got 1-(3/x) I didn't get the part how you took 1.
Did you consider the total work done as 1?
I took the Total work done as X and thus got Work done by Joseph as :  X-\frac{3}{X}

Bunuel · Answer

Yes, the whole job is 1 unit.

The question says that Lindsay can paint  \frac{3}{x}  of a room in 1 hour. If 3/x is confusing there, consider x to be say 6 and it will become easier to understand: Lindsay can paint  \frac{3}{6}=\frac{1}{2}  of a room in 1 hour. Together they paint  the whole room  in 1 hour then Joseph can paint  1-\frac{1}{2}=\frac{1}{2}  of a room in 1 hour. In 20 minute or in  \frac{1}{3}  of an hour Joseph can paint  \frac{1}{6}  of a room.

Now, plug x = 6 into the options to see which one gives you 1/6.

101mba101 · Answer

Yes, the whole job is 1 unit.

The question says that Lindsay can paint  \frac{3}{x}  of a room in 1 hour. If 3/x is confusing there, consider x to be say 6 and it will become easier to understand: Lindsay can paint  \frac{3}{6}=\frac{1}{2}  of a room in 1 hour. Together they paint  the whole room  in 1 hour then Joseph can paint  1-\frac{1}{2}=\frac{1}{2}  of a room in 1 hour. In 20 minute or in  \frac{1}{3}  of an hour Joseph can paint  \frac{1}{6}  of a room.

Now, plug x = 6 into the options to see which one gives you 1/6.

Thanks a lot Bunuel! I understood your method now. You make things very simple.

sset92 · Answer

Assume the work to be something that is easily divisible by 20 and x => 100x

Lindsay can paint 1/x of the room in 20 minutes so it means Rate of work = 100x/20x = 5/minute (Call it RL)
Now, Lindsay and Joseph together can do the work in 60 minutes so we have => (5+RJ)*60 = 100x
From this we get RJ = (5x-15)/3 per minute

In 20 minutes Rj will do 20*(5x-15)/3

Fraction of work => (20(5x-15))/3*100x => (x-3)/3x

Tejassharmaa · Answer

IF we take x = 4. We get L finishes 3/4th in 1 hour. So J does 1/4 in 1 hour. In 20 mins he will do 1/12 and option A and C both are giving 1/12. Can you please tell me where am I faultering?

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Lindsay can paint 1/x of a certain room in 20 minutes. What fraction

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