Question

A boat goes 35 km. upstream and 55 km down-stream in 12 hours. In 10
hours it can go 30 km. upstream and 44 km. down-stream. Determine the
speed of the stream and that of the boat in still water.​

Answer 1

$\rule{200}3$

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

$\rule{200}3$

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