A boatman goes $2\text{km}$ against the current of the stream in $1\text{hour}$ and goes $1\text{km}$ along the current in $10\text{minutes}$. How long will it take to go $5\text{km}$ in stationary water?

To find the time taken in stationary water, we first determine the upstream and downstream speeds of the boat.
1. **Upstream Speed ($U$):**
The boatman travels $2\text{km}$ in $1\text{hour}$ against the current.

$$U=\frac{2\text{km}}{1\text{hr}}=2\text{km/h}$$

2. **Downstream Speed ($D$):**
The boatman travels $1\text{km}$ in $10\text{minutes}$ along the current.

$$D=\frac{1\text{km}}{\frac{10}{60}\text{hr}}=6\text{km/h}$$

3. **Speed of the boat in stationary water ($B$):**

$$B=\frac{D+U}{2}=\frac{6+2}{2}=4\text{km/h}$$

4. **Time taken to travel $5\text{km}$ in stationary water:**

$$\text{Time}=\frac{\text{Distance}}{\text{Speed}}=\frac{5\text{km}}{4\text{km/h}}=1.25\text{hours}$$

Converting $0.25\text{hours}$ into minutes:

$$0.25\times 60\text{minutes}=15\text{minutes}$$

Therefore, the total time required is $1\text{hr}15\text{mins}$.