Answer: she will need 2.8 days to finish the work.
Step-by-step explanation:
Let's define:
D = number of days.
B = rate at which Barbara paints a barn
S = rate at which Sara paints a barn
We know that Barbara can paint a barn in 5 days, then:
B*5 days = 1 barn
B = 1/5 barns per day.
And we know that Sara can paint it in 8 days, then:
S*8 days = 1 barn
S = 1/8 barns per day.
Now, when they work together, their rates are added.
Then if they work together for two days, they paint a total of:
(1/5 barns per day + 1/8 barns per day)*2 days
(8/40 barns per day + 5/40 barns per day)*2 days
(13/40 barns per day)*days = 26/40 barns
Now Sara needs to paint he other 14/40 barns in her own, she will need D days, then:
(1/8 barns per day)*D = 14/40 barns
D = (14/40 barns)/(1/8 barns per day) = (14*8/40) = 2.8 days.
So she will need 2.8 days to finish the work.
