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?

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.

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