Final answer:
Jessica and her daughter have a combined work rate of 7/60 of the fence per day. After working together for 4 days, they complete 7/15 of the work. Jessica will need an additional 6.4 days to finish the remaining 8/15 of the fence by herself.
Step-by-step explanation:
To solve how long it will take for Jessica to finish building the fence by herself after working together with her daughter for 4 days, we need to calculate the rate of work when they are working together and then how much work is left after the 4 days.
Jessica completes the fence in 12 days, so her work rate is 1/12 of the fence per day. Her daughter completes the fence in 20 days, so her work rate is 1/20 of the fence per day. When they work together, their combined work rate is 1/12 + 1/20 = 4/60 + 3/60 = 7/60 of the fence per day.
In 4 days, they complete 4 * (7/60) = 28/60 of the fence, which reduces to 14/30 or 7/15 of the fence. Therefore, there is 1 - 7/15 = 8/15 of the fence left for Jessica to finish by herself.
At Jessica's work rate of 1/12 of the fence per day, to finish the remaining 8/15 of the fence it will take her (8/15) / (1/12) = 8/15 * 12/1 = 96/15 days. Simplified, this is 6.4 days. Therefore, Jessica will take an additional 6.4 days to finish building the fence on her own.