A boat travels 36 km downstream in 3 hours and returns upstream covering the same distance in 5 hours. What is the speed of boat in still water?

The correct option is 9.6 km/hour.

Let the speed of the boat in still water be _x km/hour and the speed of the stream be _y km/hour.

When the boat travels downstream, the effective speed is the sum of the speed of the boat and the speed of the stream:

$${\mathrm{Speed}}_{\mathrm{downstream}}=x+y$$

We are given that the boat travels 36 km downstream in 3 hours. Since $\mathrm{Speed}=\frac{\mathrm{Distance}}{\mathrm{Time}}$, we can write:

$$x+y=\frac{36}{3}$$

$$x+y=12$$ (Equation 1)

When the boat travels upstream, it moves against the stream, so the effective speed is the difference between the speed of the boat and the speed of the stream:

$${\mathrm{Speed}}_{\mathrm{upstream}}=x-y$$

We are given that the boat returns upstream covering the same distance (36 km) in 5 hours. Therefore:

$$x-y=\frac{36}{5}$$

$$x-y=7.2$$ (Equation 2)

To find the speed of the boat in still water (_x), we can add Equation 1 and Equation 2:

$$(x+y)+(x-y)=12+7.2$$

$$2x=19.2$$

$$x=\frac{19.2}{2}$$

$$x=9.6$$

Thus, the speed of the boat in still water is 9.6 km/hour.