Question: c is twice as fast as a and b working together, and can complete the work 4 days earlier than a and b working together. if a takes 16 days to do the work alone, how many days would b alone take?
Solution: Sure, I can help you with that.
Let's say the total work is represented by 16 units.
If A takes 16 days to do the work alone, then A can do 1 unit of work in 1 day.
Since C is twice as fast as A and B working together, then C can do 1 unit of work in half the time that A and B working together can do 1 unit of work.
Let's say the number of days it takes A and B working together to do 1 unit of work is x.
This means that C can do 1 unit of work in x/2 days.
We also know that C can complete the work 4 days earlier than A and B working together.
This means that the total number of days it takes C to complete the work is x/2 - 4.
Since the total work is represented by 16 units and C can do 1 unit of work in x/2 - 4 days, then C can complete the total work in (x/2 - 4)*16 = 8x - 64 days.
We are also given that c is twice as fast as A and B working together.
This means that the total number of days it takes A and B working together to complete the work is 8x - 64 / 2 = 4x - 32 days.
We are also given that if a takes 16 days to do the work alone, then A and B working together can finish the work in 14 days.
This means that 4x - 32 = 14
4x = 46
x = 11.5
Since x is the number of days it takes A and B working together to do 1 unit of work, then it takes A and B a total of 11.5 * 16 = 184 days to complete the total work.
Since A can do 1 unit of work in 1 day, then B can do 1/184 units of work in 1 day.
Therefore, it takes B a total of 184 days to complete the total work.
So the answer is 184