# MATH rate question

#### predentgal

It take 5 painters 12 days to pAint a certain office. How long would it take 6 painters to paint an office with 50% more wall space?

This is a kaplan problem. They give a weird exaplanation. Does anyone have a simple way to calcualate this?

#### dentalWorks

##### Nights Watchmen
7+ Year Member
Alright,

Step 1
Rate = how much work was done / total time
in other words
Rate = 1 wall / 12 days .... But this is the rate for THE WHOLE job

Step 2
We need to then determine how fast each painter works. meaning, the RATE of each painter.

Lets suppose the rate for 1 painter is X, so since we have 5 painters, we are going to have X+X+X+X+X = rate for THE WHOLE job

Lets simplify the above:
5X = 1/12...... solving for X and you have...
X = 1/60 <--this is the rate for 1 painter

Step 3
Now the easy part. The problem is giving us 6 painters, thats 6X = 6(1/60)
And the problem is also telling us that now, the wall is 50% bigger than the other wall.... so new wall = 1 + 1/2 = 1.5. The only thing we need to determine is how much time THE WHOLE JOB took to finish, lets call this value Y

Finally solve this:
6(1/60) = 1.5 / Y
and Y = 15 days

I hope this helped

OP
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#### predentgal

How did you know how to set it up like that? What I was doing was this. To get rate it would day per painter. So 12 days per 5 painters= 2.4 days for 1 painter. Now that we have 6 painters on the job I did 12 days per 6 painters and got 2 days for 1 painter. And then since its 50% as much I did 2 * 1.5= 3
The 3 * 6 painters= 18 days
I know this iswrong but why?

OP
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#### predentgal

im screwed for the the math section..when you took the real thing were the problems this hard ?

#### UCB05

How did you know how to set it up like that? What I was doing was this. To get rate it would day per painter. So 12 days per 5 painters= 2.4 days for 1 painter. Now that we have 6 painters on the job I did 12 days per 6 painters and got 2 days for 1 painter. And then since its 50% as much I did 2 * 1.5= 3
The 3 * 6 painters= 18 days
I know this iswrong but why?

12days/5 painters is not the same as 2.4days per 1 painter. Look at that closely and you'll see you're saying that 1 painter paints faster than 5 painters. You're missing a third variable, office space painted per painter per unit time.

Since your objective is office completion rate, you want your units of production to be representative of that, and because production varies directly by time AND number of workers, painter-days per office would be a good place to start. therefore it takes (12)(5)=60 painter-days per office. if your new objective is 1.5 times worth of office space, your new target will be 90 painter-days. with 1 painter it takes 90 days. with 6 painters it takes 15.

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#### predentgal

I dont get how thats not the same thing(12days/5 painters is not the same as 2.4days per 1 painter)? You said look at that closely and I'll see that I'm saying 1 painter paints faster than 5 days.. dont see it lol

How is 1 painter painting faster than 5 painters if 2.4 days * 5 painters= 12 days

Im really not trying to be a smart ass or anything I just really dont get it!! sorrry

#### Maygyver

10+ Year Member
5+ Year Member
Basically, saying 2.4 days per 1 painter is saying that 1 painter could paint the office in 2.4 days while it takes 5 painters 12 days.

Since this question involves a change in space, you also need to account for the space variable so the easiest way to set it up is figure out how much space the original office is.

Hope that helps.

#### dentalWorks

##### Nights Watchmen
7+ Year Member
problems like this are VERY common on the DAT.

When you see a rate problem... RIGHT AWAY think "Speed = miles / hour"
You see, Speed is the rate, miles is the amount of work that was done, and hour is well, the amount of time it took to get the work done.

Same thing with your above problem:
Rate = 1 office (work) / 12 days (time).

OP
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#### predentgal

I get it now...just have to continue practicing these type of problems. Thank u all