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To solve this problem, let’s define the variables and apply the concept of speed in relation to the current.

### Given:
- The boat takes \( \frac{2}{3} \) as much time to travel downstream as it does to travel upstream.
- The current's speed = 8 kph.

### Let:
- \( b \) = speed of the boat in still water (what we are trying to find).
- The speed downstream = \( b + 8 \) (boat's speed + current speed).
- The speed upstream = \( b - 8 \) (boat's speed - current speed).

### Using the Relationship Between Time, Distance, and Speed:
Since time is inversely proportional to speed for the same distance:
\[
\frac{\text{Time upstream}}{\text{Time downstream}} = \frac{3}{2}
\]

Therefore:
\[
\frac{\text{Distance} / (b - 8)}{\text{Distance} / (b + 8)} = \frac{3}{2}
\]

### Simplify the Equation
The distance terms cancel out:
\[
\frac{1}{b - 8} \times (b + 8) = \frac{3}{2}
\]

###

A boat takes 2/3 as much time to travel downstream from C to D as it does to return. If the rate of the river's current is 8 kph, what is the speed of the boat in still water?

Learn how to calculate the speed of a boat in still water when it takes 2/3 as much time to travel downstream as upstream, with a river current speed of 8 kph. This problem covers concepts in algebra, ratios, and the relationship between speed, time, and distance. Suitable for high school students.

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