The problem is written in Japanese, and I'll first translate it into English for clarity:

Problem: When a boat moves upstream, its speed is 20 km/h. However, when it moves downstream, its speed is 26 km/h. Assuming that the boat's own speed is constant, what is the speed of the river's current?

Solution Approach:

Let:

• $v_b$ be the speed of the boat in still water (without any current),
• $v_r$ be the speed of the river's current.

1. Upstream:

   • The effective speed of the boat when moving upstream is reduced by the speed of the current.
   • So, $v_b - v_r = 20 \, \text{km/h}$.

2. Downstream:

   • The effective speed of the boat when moving downstream is increased by the speed of the current.
   • So, $v_b + v_r = 26 \, \text{km/h}$.

Solving these two equations:

• $v_b - v_r = 20$ \ \ \ (Equation 1)
• $v_b + v_r = 26$ \ \ \ (Equation 2)

To find $v_r$ (the speed of the current), add Equation 1 and Equation 2:

$(v_b - v_r) + (v_b + v_r) = 20 + 26$ $2v_b = 46 \implies v_b = 23 \, \text{km/h}$

Now substitute $v_b = 23$ into Equation 2:

$23 + v_r = 26 \implies v_r = 26 - 23 = 3 \, \text{km/h}$

Conclusion:

The speed of the river's current is 3 km/h.

Would you like further explanation or details on this? Here are 5 related questions you might want to consider:

1. How is the speed of the boat calculated when moving against and with the current?
2. How can this same principle be applied to other vehicles moving in fluid mediums?
3. What if the current was non-uniform? How would the equations change?
4. How can we model this problem using vectors?
5. Could this method be extended to handle more complex river speed profiles?

Tip: Whenever dealing with relative velocities (such as boat speed in water or plane speed in wind), always account for the effect of the medium (water current, wind speed) in both directions (against and along).