Sally can paint a room in 7 hours while it taks steve 9hours to finsh the same room. how ling will it take them to paint if they worked together?

How much part can sally paint in an hour ?
a ÷ 7 = a/7

And what about Steve ?
a ÷ 9 = a/9

Where, a is the total area of the room.

So, let the time taken by both of them to paint the room together be 't'

So,
t(a/7 + a/9) = a
t(9a/63 + 7a/63) = a
t(16a/63) = a
t = 63/16 ≈ 4 hr

Sally alone can paint the room in 7 hours.

In 7 hours Sally alone does the job.

In 1 hour   Sally would do (1/7) of the job.

Steve can paint it alone in 9 hours.

In 9 hours Steve alone does the job.

In 1 hour   Steve would do (1/9) of the job.

Both working together in 1 hour would do:   (1/7) + (1/9).    

(1/7)*(9/9) + (1/9)*(7/7) = 9/63 + 7/63 = (9 + 7) / 63 = 16/63

In 1 hour both will have done (16/63) of the job.

16/63 of the job will be done in 1 hour by both.

Therefore  a 1 whole fraction of the job will be done in:   1 hour ÷ 16/63

                             =   1 hour × 63/16

                             = 63/16 hours = 3.9375 hours

It would take both 63/16 hours or 3.9375 hours.