One hose can fill a goldfish pond in 55 minutes thus it can fill 1/55 of the pond in 1 min (the rate of the first hose)

Two hoses can fill the same pond in 30 minutes thus they fill 1/30 of the pond in 1 min (the together rate of the two hose)

Let 'x' represent the minutes the second hose need to fill the pond alone

The second hose fills 1/x of the pond in 1 min (the rate of the second hose), x>0

Now we have:

1/55 + 1/x = 1/30

by solving we find:

x = 66 min

click here to see the step by step solution of the equation:

the second hose needs 66 minutes to fill the pond alone.