Let's denote the work rate of A as "A" and the work rate of B as "B." We know that A is three times as efficient as B, so we can write:

A = 3B

Now, we also know that A and B can do a work together in 18 days. The work rate of A and B combined is the sum of their individual work rates, which can be represented as:

A + B

Since they complete the work in 18 days together, we can write:

(A + B) = 1/18

Now, we want to find how long it would take B alone to complete the work. Let's denote that time as "x" days. The work rate of B alone would be:

B (work rate of B alone) = 1/x

Now, we have two equations:

A = 3B

(A + B) = 1/18

We can substitute the value of A from the first equation into the second equation:

(3B + B) = 1/18

Combine like terms:

4B = 1/18

Now, isolate B by dividing both sides by 4:

B = (1/18) / 4

B = 1/72

So, B's work rate is 1/72 of the work per day. To find how many days B alone can complete the work, take the reciprocal of B's work rate:

x (number of days for B alone) = 1 / (1/72)

x = 72

Therefore, it would take B alone 72 days to complete the work.