A painter can finish painting a house in 7 hours. Her assistant takes 9 hours to finish the same job. How long would it take for them to complete the job if they were working together?

3.9375 hours

Step-by-step explanation:

Combined time

= product of individual times : sum

= (7*9) / (7+9)

= 63/16

= 3.9375

c = 3.9375 hours

Step-by-step explanation:

The formula to determine time to finish the job together is

1/a + 1/b = 1/c

Where a and b are the times to complete the job separately and c is the time to complete the job when working together

1/7 + 1/9 = 1/c

Multiply by 63c to get rid of the fractions

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

9c + 7c = 63

Combine like terms

16c = 63

Divide each side by 16

16c/16 = 63/16

c = 3.9375 hours