Question

a boat 12 km upstream and 40 downwards in 8 hours . It can go 60 km upstream and 32km downstream in the same time . Find the speed of the boat in still water and the speed of the stream

Answer 1

Answer:

X=6 km/h

y= 2km/h

Step-by-step explanation:

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

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