Tom, Sam and Victor are painting the rooms in their new house. It takes Tom 4 hours to paint one room, but Sam and Victor take 3 hours each. If all of them work together, how long does it take them to paint one room?

1 1/12 hours to paint one room together

Step-by-step explanation:

in 4 hour no of room painted by Tom = 1

dividing both side by four to find part of room painted in 1 hour

in 4/4 hour no of room painted by Tom = 1/4

so,

in 1 hour no of room painted by Tom = 1/4

similarly

in 3 hour no of room painted by Sam and Victor = 1

dividing both side by 3 to find part of room painted in 1 hour

in 3/3 hour no of room painted by Sam and Victor each = 1/3

so,

in 1 hour no of room painted by Sam and Victor each= 1/3

Total part of room painted by all of them working together in 1 hour

= 1/4 room  + 1/3 room + 1/3room =(3 + 4+ 4)  /12= 11/12 of room

Hence,

in 1 hour they paint together = 11/12 of the room

to find time taken to paint 1 full room

we divided both side by 11/12

in 1/(11/12) hour they paint together = 11/12/(11/12) of the room

in 12/11 hours they paint together = 1 room

Thus,

they take 12/11 hours i.e. 1 1/12 hours to paint one room together.

1 hour = 60 minutes

1/12 hours = 60/12 minutes = 5 minutes

thus, we can also say

they take 1 hours and 5 minutes  to paint one room together.