Question

a boat goes 12 km upstream and 40 km downstream in 8 hrs . It can go 16 km upstream, 32 km downwards in same time . find speed of boat in still water and speed of current​

Answer 1

let speed of boat is x and stream is y

speed of boat upstream = x-y

speed of boat downstream = x+y

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

8(x²-y²) = 52x -28y ..................(1)

8 = 16/(x-y) + 32/(x+y)

8(x²-y²) = 48x - 16y ..................(2)

(1) - (2)

4x - 12y = 0

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)

y = 2Km./h   (speed of stream)

Hope it helps...

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