Question

14. A boat goes 12 km upstream and 40 km downstream in 8 hours. It can go 16km upstream
and 24km downstream in 7 hours. Find the speed of the boat in still water and the speed of the
stream.

Answer 1

Answer:

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)