Question

It takes 636363 minutes for 444 people to paint 999 walls. how many minutes does it take 777 people to paint 444 walls? minutes

Answer 1

Let t=time, p=people, and w=walls.

We know that the time it takes is directly proportional to the length of the wall but inversely proportional to the number of people working. That is

`t=k\cdot (w)/(p)`

We solve for the constant of proportionality, k.

`k=(t\cdot p)/(w)`

The initial values for k are the same for the final values. That is

`(t_1\cdot p_1)/(w_1)=(t_2\cdot p_2)/(w_2)`


`(63\cdot 4)/(9)=(t_2\cdot 7)/(4)`


`t_2=(4\cdot 63\cdot 4)/(7\cdot 9)=16`

It will take 16 minutes.