Problem Analysis: Boat Speed Calculation

The question asks for the speed of a boat in still water. We are given a relationship between the boat's downstream and upstream speeds and the speed of the river current.

• Relationship: Speed downstream is 3 times the speed upstream.
• River flow speed ($S_w$): 8 kmph.
• Find: Speed of the boat in still water ($S_b$).

Formulating Equations for Speed

Let $S_b$ represent the speed of the boat in still water and $S_w$ represent the speed of the river current.

• Downstream speed ($S_d$): $S_d = S_b + S_w$
• Upstream speed ($S_u$): $S_u = S_b - S_w$

We are given $S_w = 8$ kmph.

Applying the Downstream/Upstream Ratio

The problem states that the downstream speed is thrice the upstream speed:

$S_d = 3 \times S_u$

Substitute the expressions for $S_d$ and $S_u$:

$S_b + S_w = 3 \times (S_b - S_w)$

Solving for Boat Speed

Now, substitute the value of the river flow speed, $S_w = 8$ kmph:

$S_b + 8 = 3 \times (S_b - 8)$

Expand the equation:

$S_b + 8 = 3S_b - 24$

Rearrange the terms to solve for $S_b$:

$8 + 24 = 3S_b - S_b$

$32 = 2S_b$

Calculate the speed of the boat in still water:

$S_b = \frac{32}{2}$

$S_b = 16 \text{ kmph}$