Concept Based on Boats and Rivers

The present study has discussed the concepts of boats and rivers. It is one of the most common topics used in mathematics, in order to solve the mathematical problems related to boats and streams. This study also includes different formulas related to the concepts of boats and rivers. In addition, it also includes some solved questions and answers related to the current topic. 

Concepts of boats and rivers

The concepts of boats and rivers deal with the time that is taken by a boat in order to cover a specific distance. That way the calculation is done for getting the results. In order to understand the concepts of boats and rivers an individual needs to understand some basic terms such as speed of the boat, still water, stream, downstream, and upstream and brings favourable growth in mathematics 

Still water: the water of a river or any other water body, which is not flowing, is called still water.  

Speed of a boat: it means the speed of the boat in still water.

Stream: when the water of the river is flowing in a particular direction then it is said to be a stream.  

Downstream: when the boat is moving in the direction of the stream then it is called downstream.

Upstream: when the boat is moving in the opposite direction of the water flow.

Other terms that are mentioned above are very important for solving different problems that are related to boats and streams. From the concepts of boats and rivers, various types of questions can be asked such as time-based questions, speed-based questions, and questions on average speed, and questions based on the distance covered. 

Formulas of boats and stream

Each term used above has a different mathematical formula, where u is the speed of a boat in still water and v is the speed of a stream. 

• Upstream = (u – v) km/hr
• Downstream = (u + v) km/hr 
• Speed of stream = ½ (downstream speed – upstream speed)
• Speed of boat in still water = ½ (Downstream + Upstream)Speed
• The average speed of boat = {(Upstream speed * Downstream speed)/ speed of boat in still water}
• If t times take for a boat to reach a point in still water and come back to the same points then the distance between the two pints can be calculated as 

Distance = {(u2 – v2) * t / 2u

• If a boat takes time to go to a point upstream and comes back downstream for the same distance then the formula of distance = {(u2 – v2) × t} / 2v.
• If a boat travels a distance in t1 hours and comes back the same distance upstream in t2 hours then the speed of the boat in still water is = [v × {(t2+t1) / (t2-t1)}] km/hr. 

Mathematical Examples of boats and river 

There are different kinds of questions such as time-based and speed based in this method. In addition, questions can be regarded at every speed and based on distance as well. In the case of time-based questions, the time that is taken by a boat for traveling upstream or downstream can be asked in accordance with the speed of a boat in still water as well as the speed of the boat in a stream.

For example, a question can be:

• • Per hour, a boat goes 10 km/hr downstream and 6 km/hr upstream. What is the boat’s speed in still water?
  • Answer: Boat’s speed in still water = ½ (Downstream Speed + Upstream Speed)

• Speed of boat in still water = ½ (10+6) = ½ × 16 = 8 km/hr

  Conclusion 

  As per the above analysis, it can be concluded that boat and stream questions are basic time and distance-related questions that are taught to the intermediary level students in India. On the other hand, boat and stream questions can help students to build a basic knowledge on time and distance that they can use for that study. In practical life, experience-based questions come into action as well and help students understand the value of time and distance equations.