Given that, two girls, j and k take two hours to sweep the school compound, if k alone takes 3 hours to sweep compound working at same rate, how long does j takes if she works alone?

Let's first find the rate at which both girls work together.

Let the rate at which girl j works be x and the rate at which girl k works be y.

From the given information, we know that:
1/x + 1/y = 1/2 (since they take 2 hours to sweep the compound together)
1/y = 1/3 (since girl k takes 3 hours to sweep the compound alone)

Substitute 1/y = 1/3 into the first equation:
1/x + 1/3 = 1/2
1/x = 1/2 - 1/3
1/x = 3/6 - 2/6
1/x = 1/6

Therefore, girl j takes 6 hours to sweep the compound alone.

Let's assume that j takes x hours to sweep the compound if she works alone.

When j and k work together, they can sweep the compound in 2 hours. So, their combined rate of work is 1/2 of the compound per hour.

Since k takes 3 hours to sweep the compound alone, his rate of work is 1/3 of the compound per hour.

Therefore, j's rate of work is:

(1/2) - (1/3) = 1/6 of the compound per hour

To find how long j takes if she works alone, we can use the formula:

Time = Work / Rate

Since j needs to sweep the entire compound, the work is 1 compound.

So, the time j takes to sweep the compound alone is:

Time = 1 / (1/6) = 6 hours

Therefore, j takes 6 hours to sweep the compound if she works alone.