Solving Boat Speed in Still Water Problems

This problem involves calculating the speed of a boat in still water using its downstream and upstream travel information.

Formulating Equations

Let '\(s_b\)' be the speed of the boat in still water (in km/hr) and '\(s_w\)' be the speed of the stream (in km/hr).

• Downstream speed = Speed of boat + Speed of stream = \(s_b + s_w\)
• Upstream speed = Speed of boat - Speed of stream = \(s_b - s_w\)

Calculating Speeds

We use the formula: Speed = Distance / Time.

• Downstream Speed: The boat covers 18 km in 3 hours downstream.

  Downstream speed = \(\frac{18 \text{ km}}{3 \text{ hours}} = 6\) km/hr.

  Therefore, \(s_b + s_w = 6\) (Equation 1).

• Upstream Speed: The boat covers 18 km in 9 hours upstream.

  Upstream speed = \(\frac{18 \text{ km}}{9 \text{ hours}} = 2\) km/hr.

  Therefore, \(s_b - s_w = 2\) (Equation 2).

Finding Boat Speed in Still Water

To find '\(s_b\)', we solve the system of two linear equations:

1. Add Equation 1 and Equation 2:

   \((s_b + s_w) + (s_b - s_w) = 6 + 2\)

   \(2s_b = 8\)

2. Solve for \(s_b\):

   \(s_b = \frac{8}{2}\)

   \(s_b = 4\) km/hr

The speed of the boat in still water is 4 km/hr.