Problem 1. “part a)” is exactly the same problem as the one on the following link. Just in your case, Worker A is their Worker B, and your Worker B is their Worker A…. but it doesn’t really matter who is A or who is B… at least for the part a) part of the problem…

http://www.purplemath.com/modules/printpage.cgi?path=/modules/workprob.htm

Read the above link and see if their explanation helps…

Then come back here and read the solution that I’ve adjusted a bit…

If the first painter can do the entire job in 8 hours and the second painter can do it in 12 hours, then (this here is the trick!) the first guy can do 1/8 of the job per hour, and the second guy can do 1/12 per hour. How much then can they do per hour if they work together?

To find out how much they can do together per hour, I add together what they can do individually per hour: 1/8 + 1/12 = 5/24. They can do 5/24 of the job per hour. Now I’ll let “t” stand for how long they take to do the job together. Then they can do 1/t per hour, so 5/24 = 1/t. Flip the equation, and you get that t = 24/5 = 4.8 hours. That is:

hours to complete job:

first painter: 8

second painter: 12

together: t

completed per hour:

first painter: 1/8

second painter: 1/12

together: 1/t

adding their labor:

1/8 + 1/12 = 1/t

5/24 = 1/t

24/5 = t

They can complete the job together in just under 5 hours.

A: 1/8

B: 1/12

Working together, the time to complete the entire job is:

1/8 + 1/12 = 1/t

(3/24) + (2/24) = 5/24

5/24 = 1/t

t = (24/5) = 4 4/5 days.

b) Let ‘x’ denote the portion of the job B completes in 3 days.

x/3 = 1/12

x = 3/12 = 1/4

A completes (3/4) of the job. Let ‘x’ denote the number of days required to complete (3/4) of the job:

(3/4) / x = 1/8

x = (3/4) * (8) = 6 days.

say the job takes 24 units of work to complete. I picked this number at random cuz it’s easy to work with on this problem. Worker A does 3 units of work per day to finish the job in 8 days, and Worker B would do 2 units of work per day, because it takes him 12 days to finish. now:

a) if they’re both working together each day, that’s five units of work that’s getting completed each day (A’s 3 plus B’s 2), so it takes almost six days: 5.8 days (24 total units of work for the job divided by five units per day).

b) if B works alone for 3 days, 6 units of work would get done (B does 2 units per day, according to this model), leaving 18 units to be done. A will finish the remaining work in 6 days as A can do 3 ‘units’ per day. answer: 6 more days.

b) it will take b 3 days to finish the work

idk im really rong thats a hard quetsion