A boat can travel 10 km upstream and 20 km downstream in 7 hours. It can travel 20 km upstream and 10 km downstream in 11 hours. What is the speed of the boat in still water?

Let's assume the speed of the boat in still water and the speed of the stream are B and C respectively.

upstream speed = (B-C)

downstream speed = (B+C)

A boat can travel 10 km upstream and 20 km downstream in 7 hours.

$$\frac{10}{B-C}+\frac{20}{B+C}\ = 7$$    Eq.(i)

It can travel 20 km upstream and 10 km downstream in 11 hours.

$$\frac{20}{B-C}+\frac{10}{B+C}\ = 11$$    Eq.(ii)

Multiply Eq.(i) by 2.

$$\frac{20}{B-C}+\frac{40}{B+C}\ =14$$    Eq.(iii)

Substract Eq.(ii) from Eq.(iii).

$$\frac{20}{B-C}+\frac{40}{B+C} - \frac{20}{B-C} - \frac{10}{B+C} =14-11$$

$$\frac{40}{B+C} - \frac{10}{B+C}\ =3$$

$$\frac{30}{B+C} =3$$

B+C = 10    Eq.(iv)

Put Eq.(iv) in Eq.(i).

$$\frac{10}{B-C}+\frac{20}{10}\ = 7$$

$$\frac{10}{B-C}+2\ =7$$

$$\frac{10}{B-C}\ =7-2$$

$$\frac{10}{B-C}\ =5$$

B-C = 2    Eq.(v)

Add Eq.(iv) and Eq.(v).

B+C+B-C = 10+2

2B = 12

Speed of the boat in still water = B = 6 km/h