let

x = the speed of the river

v = 8km/h the speed of the paddle boat

the speed upstream = v - x

the speed downstream = v + x

speed = distance/time => time distance / speed

he boat is paddled 6km downstream in a river in the same time it takes to go 3 km upstrea

the time going 6km downstream = the time going 3 km upstream

6/(v + x) = 3/(v - x)

6/(8 + x) = 3/(8 - x) multiply both sides by (8 + x)(8 - x)

6(8 - x) = 3(8 + x)

48 - 6x = 24 + 3x

6x + 3x = 48 - 24

3x = 24

x = 8 km/h

the speed of the river is 8 km/h.