if 15 workers can paint 18 houses in 24 days, how many days will 40 workers take to paint 22 houses?

Question

major help required!! have forgotten how to do mental math questions. showing the working would be excellent thankyou

Answer 1

If there are more workers on job, time taken is lower so

18 houses / 15 workers = 24 days * Dfactor
and
22 houses / 40 workers= Xdays * Dfactor

Calculate Dfactor through the first equation.
18houses / 15 workers / 24days = 0.05
Dfactor= 0.05

so 22 houses/ 40 workers = Xdays * 0.05

number of days : 22 / 0.05 / 40 = 11 days

Answer 2

The point is you need to remember the basic maths then you will always get this right in future.
You start with the the days, as that is what you want - 24
Then you go to each factor & ask if the change you have will increase or decrease you answer. So 22 houses take longer than 18, so 22 goes on the top & 18 on the bottom ie:24*22/18.
Now the workers, 40 workers finish the job faster so you devide by the 40 & multiply by the 15.
ie: 24*22*15/(18*40) that gives you 11 days.

Answer 3

Let
x = number of worker days to paint one house
d = days for 40 workers to paint 22 houses

18x = 15*24 = 360
x = 20 worker days / house

d = 22x/40 = 22*20/40 = 11 days

It will take 11 days for 40 workers to paint 22 houses.

Answer 4

let x = to the number of days the workers can paint the 22 houses

15 workers / 18 houses = 24 days
40 workers / 22 houses = x

therefore.

x = (40/22)(24) / (15/18)
= 52.363638 days

Answer 5

15 workers--18 houses --24days
40 workers--22 houses---24 x 15/40 x 22/18 = 11 days

Answer 6

well well well... this is no mental math questions, you can simply solve it by proportion method which is always used in science to find out the relations of different variables:

Let the number of workers = W, number of houses = H, number of days = D

Now tell me wat's the relationship of W and H, is it direct or reciprocal? Yeap, more workers means more house, so W is proportional to H.

How about W and D? Yeap, more workers means less days, so W is invert proportional to D.

Put it in mathematical way: W prop. H, W prop. 1/D, thus W prop. H/D. Now to make the prop. sign into = sign, we'll need to put a constant: W=(kH)/D.

Let's find the value of k with the values given: 15=(k*18)/24, therefore k=(15*24)/18 = 20.

TAADAA!!! We now have a mathematical formula to relate W, D and H, i.e. W=(20H)/D

The rest will be too easy to mention, just throw the values in and you'll get the answer in no time: 40=(20*22)/D, thus D = (20*22)/40 = 11 DAYS!!!

Answer 7

18/15*24*22/40

Answer 8

Well, how many houses does one worker produce in one day?

House/ (days * workers) = 18/(24*15) = Const.

new situation is

22/(days*40) = Const.

22 = days*40*Const

days = 22/(40*Const)

days = 11

Answer 9

(15/40) x (22/18) x 24 or about as long as it takes a cockroach to crawl backwards through a bar of soap.

Answer 10

15 workers 18 houses 24 days
40 workers 22 houses x days
-------------------------------------------
x=15*24*18/(40*22)=81/11 days.

answer: 8 days