A reservoir can be completely filled in $18\text{hours}$ by an inlet pipe. A leakage pipe can empty the full reservoir in $36\text{hours}$. If both pipes are opened together, find the time required to fill the reservoir.

Given:
Time taken by inlet pipe to fill the reservoir ($T_1$) = $18\text{hours}$
Time taken by leakage pipe to empty the reservoir ($T_2$) = $36\text{hours}$

Rate of filling by the inlet pipe = $+\frac{1}{18}$ per hour
Rate of emptying by the leakage pipe = $-\frac{1}{36}$ per hour

When both pipes are opened together, the net rate of filling per hour is:

$$\text{Net Rate}=\frac{1}{18}-\frac{1}{36}$$

Take LCM of $18$ and $36$, which is $36$:

$$\text{Net Rate}=\frac{2-1}{36}=\frac{1}{36}$$

Therefore, the total time required to completely fill the reservoir is the reciprocal of the net rate:

$$\text{Total Time}=36\text{hours}$$