Question

A boat goes 12 metre upstream and 40 km downstream in 8 hours it can go 16 km upstream and 32 km downstream in the same time find the speed of the boat in still water and steam of the stream

Answer 1

let speed of boat be  x and speed of stream be y

speed of boat upstream = x-y

speed of boat downstream = x+y

12/(x-y) + 40/(x+y) = 8

8(x²-y²) = 52x -28y ..................(1)   [LCM (x-y)(x+y)]

16/(x-y) + 32/(x+y) =8

8(x²-y²) = 48x - 16y ..................(2)  [LCM (x-y)(x+y)]

subtracting eq (1) - (2) we get

8(x²-y²) = 52x -28y

8(x²-y²) = 48x -16y

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     0    =   4x - 12y

x = 3y  .........................(3)   put in equation (1)

8(9y²-y²) = 52*3y - 28y

64y² = 128y

y = 0 or 2

y= 0 not possible

put y = 2 in equation (3)

x = 6Km./h   (speed of boat in still water) ANS

y = 2Km./h   (speed of stream)                   ANS

Answer 2

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