Answer:

Speed of stream = 3 km / hr.

Speed of boat in still water = 8 km / hr.

Step-by-step explanation:

Let the speed of the boat in still water be a km / hr and stream be b km / hr

For upstream = a - b

For downstream = a + b

We know :

Speed = Distance / Time

Case 1 .

10 = 30 / a - b + 44 / a + b

Let 1 / a - b = x and 1 / a + b = y

30 x + 44 y = 10 ... ( i )

Case 2 .

13 = 40 / a - b + 55 / a + b

40 x + 55 y = 13 ... ( i )

Multiply by 4 in ( i ) and by 3 in ( ii )

120 x + 176 y = 40

120 x = 40 - 176 y ... ( iii )

120 x + 165 y = 39

120 = 39 - 165 y ... ( iv )

From ( iii )  and  ( iv )

40 - 176 y = 39 - 165 y

11 y = 1

y = 1 / 11

120 x = 40 - 176 y

120 x = 40 - 176 / 11

x = 1 / 5

Now :

1 / a - b = 1 / 5

a - b = 5

a = 5 + b ... ( v )

1 / a + b = 1 / 11

a + b = 11

a = 11 - b ... ( vi )  

From ( v  ) and ( vi )

11 - b = 5  + b

2 b = 6

b = 3

a = 5 + b

a = 5 + 3

a = 8

Hence we get answer.