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Let b be the speed of the boat ; 
      c be the speed river's flow (aka current)

Remember that distance = speed x time

When the boat travels downstream, it goes with the current. Thus, its speed is increased.
The downstream travel is represented by the equation   
2 (b+c) = 64    (2 hours is the amount of time it traveled; 64 is the total distance traveled)

On the other hand, when it travels upstream, the boat goes against the current. Thus, its speed is decreased. This is shown by the equation
3 (b-c) = 54    (it took 3 hours to travel 54 km)

We now have a system of equation with two variables.

2b + 2c = 64     ––>     b + c = 32
3b - 3c = 54     ––>      b - c = 27
                                     2b      = 59

b = 59/2 = 29.5 
c = 2.5

Therefore, the rate of the river's flow is 2.5 km/hour