Boat Speed Calculations Explained

This problem involves calculating the total time taken for a boat journey that includes traveling downstream and then upstream. To solve this, we need to understand how the speed of the stream affects the boat's speed in different directions.

Understanding Boat Speeds

Key concepts for solving boat and stream problems:

• Speed in Still Water: This is the speed of the boat without any influence from the current. Given as 10 km/h.
• Speed of the Stream: This is the speed of the water current. Given as 3 km/h.
• Downstream Speed: When the boat travels with the current, the stream helps the boat. So, the downstream speed is the sum of the boat's speed and the stream's speed.
  Formula: Speed Downstream = Speed of Boat + Speed of Stream
• Upstream Speed: When the boat travels against the current, the stream opposes the boat's motion. So, the upstream speed is the difference between the boat's speed and the stream's speed.
  Formula: Speed Upstream = Speed of Boat - Speed of Stream

Calculating Downstream Travel

First, let's calculate the boat's speed when traveling downstream.

• Speed of Boat = 10 km/h
• Speed of Stream = 3 km/h
• Downstream Speed = $10 \text{ km/h} + 3 \text{ km/h} = 13 \text{ km/h}$

The distance to travel downstream is 39 km. We can calculate the time taken using the formula: Time = Distance / Speed.

• Distance Downstream = 39 km
• Downstream Speed = 13 km/h
• Time Downstream = $\frac{39 \text{ km}}{13 \text{ km/h}} = 3 \text{ hours}$

Calculating Upstream Travel

Next, let's calculate the boat's speed when traveling upstream.

• Speed of Boat = 10 km/h
• Speed of Stream = 3 km/h
• Upstream Speed = $10 \text{ km/h} - 3 \text{ km/h} = 7 \text{ km/h}$

The distance to travel upstream on the return journey is 28 km. We calculate the time taken using the same formula: Time = Distance / Speed.

• Distance Upstream = 28 km
• Upstream Speed = 7 km/h
• Time Upstream = $\frac{28 \text{ km}}{7 \text{ km/h}} = 4 \text{ hours}$

Total Journey Time

Finally, to find the total time for the entire journey (downstream and then upstream), we add the time taken for each part.

• Time Downstream = 3 hours
• Time Upstream = 4 hours
• Total Time = Time Downstream + Time Upstream
• Total Time = $3 \text{ hours} + 4 \text{ hours} = 7 \text{ hours}$

Therefore, the boat will take a total of 7 hours to complete the journey of sailing 39 km downstream and returning 28 km upstream.