Let c represent the speed of the current.
time = distance / speed
total time = time going upriver + time going downriver
2 2/3 = 6/(9 -c) + 6/c
(8/3)(c)(9 -c) = 6c +6(9 -c)
(8/3)c^2 -24c +54 = 0
c = (24 ± √((-24)^2 -4(8/3)(54)))/(2*8/3)
.. = (3/16)(24)
c = 4.5
The speed of the river's current is 4.5 km/h.
time = distance / speed
total time = time going upriver + time going downriver
2 2/3 = 6/(9 -c) + 6/c
(8/3)(c)(9 -c) = 6c +6(9 -c)
(8/3)c^2 -24c +54 = 0
c = (24 ± √((-24)^2 -4(8/3)(54)))/(2*8/3)
.. = (3/16)(24)
c = 4.5
The speed of the river's current is 4.5 km/h.