Question

a Boat goes 30 km upstream and 44 km downstream in 10 hours in 13 hours it can go 40 km upstream and 55 km downstream determine
the speed of the stream and that of the boat in still water

Answer 1

let the speed of stream be x km/hr
speed of boat y km/hr
speed in upstream= (y-x) km/hr
speed in downstream= (y+x) km/hr
ATQ
$\frac{30}{y - x} + \frac{44}{y + x} = 10 \\ \frac{40}{y - x} + \frac{55}{y + x} = 13$
$put \: \frac{1}{y - x} = u \: and \: \frac{1}{y + x} = v \\ \\ 30u + 44v = 10 \\ 40u + 55v = 13$
solving for u and v

$v = \frac{1}{11} and \: u = \frac{1}{5}$
$\frac{1}{y - x} = \frac{1}{5 } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \frac{ 1}{y + x} = \frac{1}{11} \\ y - x = 5 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: y + x = 11 \\ now \: solvingfor \: x \: and \: y \: we \: get \\ \\ y = 8 \: \: \: \: and \: x = 3 \\ \\ speed \: of \: boat \ = 8km/hr\\ \\ speed \: of \: stream = 3 km/hr$

Answer 2

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.