Math, asked by AbhiKumar1126, 10 months ago

satisfied.
Example 19 : A boat goes 30 km
upstream and 44 km downstream in
10 hours. In 13 hours, it can go
air o 40 km upstream and 55 km
down-stream. Determine the speed
of the stream and that of the boat in
still water.​

Answers

Answered by ashfaqali2004
1

Answer:

v = 8 kmph    and  u = 3 kmph

Step-by-step explanation:

Let the speed of the stream be = u kmph

let the speed of the boat be = v kmph

speed upstream will be = v - u  kmph

speed downstream will be =  v + u  kmph

30 km  upstream in time duration  =   30 / (v - u)  hrs

44 km  down stream in time duration  =  44 / (v + u)  hrs

      44 / (v + u)  + 30 / (v -u)  = 10 hrs     --- (1)

Similarly,

     40 /(v - u)  + 55 / (v +u)  = 13 hrs         Multiply with 3/4:  

     30/(v-u) + 165 / 4(v+u) =    39/4        --- (2) 

Now (1) - (2)  =>    [44 - 165/4] / (v+u) = 10 - 39/4 = 1/4

                  =>     v + u = 11      --- (3)

Substitute this in (1) to get: 

            44/11 + 30/(v-u) = 10

          =>  v - u = 30/6 = 5      --- (4)

Solving  (3) and (4) ,  we get :  v = 8 kmph    and  u = 3 kmph

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Answered by BendingReality
1

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.

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