Question

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?

Answer 1

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.

Answer 2

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