Boat Speed Calculation: Downstream & Upstream

This problem requires calculating the speed of a boat in still water using information about its travel time downstream and upstream, along with the speed of the current.

Calculating Speeds

First, calculate the downstream and upstream speeds using the formula:

$ Speed = \frac{Distance}{Time} $

• Downstream Speed: The boat travels 120 km in 6 hours downstream.

  $ Speed_{downstream} = \frac{120 \text{ km}}{6 \text{ hours}} = 20 \text{ km/hr} $

• Upstream Speed: The boat travels 120 km in 10 hours upstream.

  $ Speed_{upstream} = \frac{120 \text{ km}}{10 \text{ hours}} = 12 \text{ km/hr} $

Determining Boat Speed in Still Water

Let '$B$' represent the speed of the boat in still water and '$C$' represent the speed of the current. We know:

• Downstream speed: $B + C = Speed_{downstream}$
• Upstream speed: $B - C = Speed_{upstream}$

We are given that the speed of the current ($C$) is 4 km/hr.

Substitute the calculated speeds and the given current speed into the equations:

• Equation 1: $B + 4 \text{ km/hr} = 20 \text{ km/hr}$
• Equation 2: $B - 4 \text{ km/hr} = 12 \text{ km/hr}$

Solving either equation for $B$ gives the speed of the boat in still water:

• From Equation 1: $B = 20 \text{ km/hr} - 4 \text{ km/hr} = 16 \text{ km/hr}$
• From Equation 2: $B = 12 \text{ km/hr} + 4 \text{ km/hr} = 16 \text{ km/hr}$

Both equations confirm that the speed of the boat in still water is 16 km/hr.