Explanation
A is 4 times as fast as B, so A's rate of work is 4 times B's rate of work.
Since A finishes the work in 45 days less than B, let's assume B takes x days to finish the work. Then A takes x - 45 days to finish the work.
Since A is 4 times as fast as B, A's rate of work is 4 times B's rate of work. So, A's time to finish the work is 1/4 of B's time.
We can set up an equation based on the above: x - 45 = (1/4)x
Solve for x: x - 45 = (1/4)x --> 4x - 180 = x --> 3x = 180 --> x = 60
So B takes 60 days to finish the work, and A takes 60 - 45 = 15 days to finish the work.
Since A and B work together, their combined rate of work is the sum of their individual rates. Let's find their individual rates.
B's rate = 1/60 (work done per day)
A's rate = 1/15 (work done per day)
Combined rate = (1/60 + 1/15) = (1/60 + 4/60) = 5/60 = 1/12
So A and B together can complete the work in 12 days.
