Question

 A boat goes 12 km upstream and 40 km downstream in 8 hours. It can go 16 km upstream and 32 km downstream is the same time. Find the speed of the boat in still water and the speed of the stream.

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)

Answer 2

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

____________________

     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