A paddle boat can move at a speed of 6 ​km/h in still water. The boat is paddled 18 km downstream in a river in the same time it takes to go 9 km upstream. What is the speed of the​ river

Question

A paddle boat can move at a speed of 6 ​km/h in still water. The boat is paddled 18 km downstream in a river in the same time it takes to go 9 km upstream. What is the speed of the​ river

Answer 1

6 km/hr

same time to go 18 km downstream as 9 km upstream

d=rt

t=d/r = 18/(6+x) = 9/(6-x)

12+2x = 6-x

3x = 6

x = 2 km/hr

Answer 2

Let x be the speed of the river in km/h. Since speed is distance/time, then time is distance/speed. Since the time to travel downstream 18km at a speed of (6+x) km/h is the same as the time it takes to travel 9km at a speed of (6-x) km/h, we can represent this as a proportion:

Time = (Distance Downstream)/(Speed Downstream) = (Distance Upstream)/(Speed Upstream)

18/(6+x) = 9/(6-x)

18(6-x) = 9(6+x)

108-18x = 54+9x

54 = 27x

2 = x

Therefore, the speed of the river is 2 km/h

Hope this helped!