It takes 1.5 hours for 4 workers to paint the same room
Solution:
Given that 3 workers can paint a room in 2 hours
To find: Time taken for 4 workers to paint the same room
Assume the time needed to paint the room is inversely proportional to the number of worker
[tex]time $ \propto \frac{1}{\text { number of workers }}\\\\time =k \times \frac{1}{\text { number of workers }}[/tex]
Where, "k" is the constant of proportionality
3 workers can paint a room in 2 hours
Substitute number of workers = 3 and time = 2 hours
[tex]time =k \times \frac{1}{\text { number of workers }}\\\\2 = k \times \frac{1}{3}\\\\k = 6[/tex]
Therefore,
[tex]\text {time}=6 \times \frac{1}{\text { number of workers }}[/tex]
To find time taken for 4 workers to paint the same room, substitute number of workers = 4 in above expression
[tex]time = 6 \times \frac{1}{4} = 1.5[/tex]
Thus it takes 1.5 hours for 4 workers to paint the same room
