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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 down- stream. Determine the speed and that pf the boat in still water....????kindly explain this question....

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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