Question

A boat goes 30 km upstream and 44 km
downstream in 10 hours. In 13 hour it can go
40 km upstream and 55 km downstream. If
speed of the boat in still water is x km/hr and
speed of stream be y km/hr, then

Answer 1

$\mathfrak{\huge{Hi!}}$

$\sf{Speed\:of\:boat = x\:km/hr}$

$\sf{Speed\:of\:stream = y\:km/hr}$

C A S E 1

Upstream = 30 km (speed = x - y km/hr)

Downstream = 44 km (speed = x + y km/hr)

Total time taken = 10 hrs

Equation Formed :-

$\tt{\frac{30}{x - y} + \frac{44}{x + y} = 10}$

C A S E 2

Upstream = 40 km (speed = x - y km/hr)

Downstream = 55 km (speed = x + y km/hr)

Total time taken = 13 hrs

Equation Formed :-

$\tt{\frac{40}{x - y} + \frac{55}{x + y} = 13}$

Let's assume :- $\sf{\frac{1}{x - y} = m}$

$\sf{\frac{1}{x + y} = n}$

Equations become :-

$\sf{ \bigstar 30m + 44n = 10}$ ...(1)

$\sf{ \bigstar 40m + 55n = 13}$ ...(2)

Find the value of m from (1) :

$\sf{m = \frac{10 - 44n}{30}}$

Find the value of n from (2) :

$\sf{m = \frac{13 - 55n}{40}}$

=》 m = m

=》 $\tt{\frac{10 - 44n}{30} = \frac{13 - 55n}{40}}$

=》 $\sf{n = \frac{1}{11}}$

Put this value in any of the equation and the value of m will be :

=》 $\sf{m = \frac{1}{5}}$

By our assumptions, we get :-

x + y = 11

x - y = 5

-------

2x = 16

=》 x = 8 km/hr

y = 11 - 8 = 3 km/hr

$\boxed{\bf{x = Boat's\: speed = 8\:km/hr}}$

$\boxed{\bf{y = Stream's\:speed = 3\:km/hr}}$

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.