Question

a boat goes 30 km upstream and 44 km downstream in 10 hrs . in 30 hrs , 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

Answer:

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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1

Answer

Step-by-step explanation:

Answer 2

Let us assume that the speed of the stream is s km / hr and the speed of the boat is a km / hr .

Speed of the boat upstream :

> ( a - s) km / hr

Speed of the boat downstream :

> ( a + s) km / hr

The boat can go 30 km upstream in 10 hours .

( a - s) = [ Distance_1/T_1 ] = 3 km p h ... [1]

The boat goes 44 km downstream in 10 hours .

(a + s) = [ Distance_2/T_2 ] = 4.4 km p h .... [2]

Adding the two equations :

> 2 a = 7.4 km p h

> a = 3.7 km p h

> s = 0.7 km p h

Answer :

The speed of the boat in still water is 3.7 kilometers per hour and the speed of the stream is 0.7 kilometers per hour downstream .

Some of the information given in the question is redundant.

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