# 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 of the stream and that of the boat in still water.

1
by jaisdiksha

2015-05-01T02:04:26+05:30

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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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