1. ## Working Alone

Patrice, by himself, can paint 4 rooms in 10 hours. If he hires April to help, they can do the same job together in 6 hours. If he lets April work alone, how long will it take her to paint the room?

Let x = length of time it will take April to paint the room alone.

Patrice = 1/10

April = 1/x

Together = 1/6

(1/10) + (1/x) = (1/6)

Correct?

2. ## Re: Working Alone

Yes, that is the correct equation but it would better to say what
"Patrice = 1/10
April = 1/x
Together = 1/6"

MEAN!

3. ## Re: Working Alone

Originally Posted by harpazo
Patrice, by himself, can paint 4 rooms in 10 hours. If he hires April to help, they can do the same job together in 6 hours. If he lets April work alone, how long will it take her to paint the room?
Let x = length of time it will take April to paint the room alone.
Patrice = 1/10
April = 1/x
Together = 1/6
(1/10) + (1/x) = (1/6)
Correct?
What happened to the four rooms? Where are they in the setup?

4. ## Re: Working Alone

Apparently "the job" consists of painting 4 rooms. Since the problem asks about "the job" the individual rooms are irrelevant.

But, yes, the wording should be "If he lets April work alone, how long will it take her to do the job and
"Let x= the length of time it would April to do the job alone"

and to say:
The rate at which Patrice works= 1/10
The rate at which April works= 1/x
The rate at which they work together= 1/6.

(I hate wording like "Patrice= 1/10" and "April= 1/x". Patrice and April are people, not numbers!)

5. ## Re: Working Alone

Originally Posted by harpazo
Patrice, by himself, can paint 4 rooms in 10 hours. If he hires April to help, they can do the same job together in 6 hours.
If he lets April work alone, how long will it take her to paint the room?
Originally Posted by HallsofIvy
Apparently "the job" consists of painting 4 rooms. Since the problem asks about "the job" the individual rooms are irrelevant.
Actually it does say "If he lets April work alone, how long will it take her to paint the room one room.

6. ## Re: Working Alone

Originally Posted by harpazo
Patrice, by himself, can paint 4 rooms in 10 hours. If he hires April to help, they can do the same job together in 6 hours.
If he lets April work alone, how long will it take her to paint the rooms?

Let x = length of time it will take April to paint the rooms alone.
.
.
.
harpazo, the first time around the word "rooms" was used. So, it makes sense that "rooms" would continue to be used, not "room" and especially
not "the room," because there is no distinct/particular room.

7. ## Re: Working Alone

Originally Posted by HallsofIvy
Yes, that is the correct equation but it would better to say what
"Patrice = 1/10
April = 1/x
Together = 1/6"

MEAN!
Originally Posted by Plato
What happened to the four rooms? Where are they in the setup?
I don't know what this means. I am just following the examples for this particular question.

8. ## Re: Working Alone

(1/10) + (1/x) = (1/6)

3x + 30 = 5x

3x - 5x = -30

-2x = -30

x = -30/-2

x = 15

Alone, April can paint four rooms in 15 hours.