Boats and Streams

Boat and Stream – Concept

There is a wide range of concepts about boats and streams problems. Some of the major concepts related to boats and streams are mentioned below:

  • Stream – A stream is used to refer to running river water.
  • Upstream – When the boat rows or moves in the opposite direction of the flow of the stream, it is said to be moving upstream. The boat’s net speed, in this case, is upstream speed.
  • Downstream – When the boat rows or moves along the direction of the flow of the stream, it is said to be moving downstream. The boat’s net speed, in this case, is downstream speed.
  • Still Water – Still water is the assumption of water being still or stationary. This happens when the speed of the water is zero.

Upstream and Downstream – Formula

Below are the important formulas for the various boats and streams concepts.

  • Upstream = (u−v) km/hr, where “u” is the speed of the boat in still water and “v” is the speed of the stream
  • Downstream = (u+v)Km/hr, where “u” is the speed of the boat in still water and “v” is the speed of the stream
  • Speed of Boat in Still Water = ½ (Downstream Speed + Upstream Speed)
  • Speed of Stream = ½ (Downstream Speed – Upstream Speed)
  • Average Speed of Boat = {(Upstream Speed × Downstream Speed) / Boat’s Speed in Stii Water}
  • If it takes “t” hours for a boat to reach a point in still water and comes back to the same point then, the distance between the two points can be calculated by Distance = {(u2-v2) × t} / 2u, where “u” is the speed of the boat in still water and “v” is the speed of the stream
  • If it takes “t” hours more to go to a point upstream than downstream for the same distance, the formula for distance will be: Distance = {(u2-v2) × t} / 2v, where “u” is the speed of the boat in still water and “v” is the speed of the stream
  • If a boat travels a distance downstream in “t1” hours and returns the same distance upstream in “t2” hours, then the speed of the man in still water will be: Speed of Man in Still Water = [v × {(t2+t1) / (t2-t1)}] km/hr, where“v” is the speed of the stream

Types of Questions

The questions from this topic may usually be asked in four different formats. These include:

  • Time Based Questions – The time taken by a boat to travel upstream or downstream may be asked with the speed of a boat in still water and speed of the stream given in the question
  • Speed Based Questions – Questions to find the speed of the stream or the speed of the boat in still water may be asked 
  • Questions on Average Speed – With the speed of the boat upstream and downstream given in the question, the average speed of the boat may be asked
  • Questions Based on Distance – The distance travelled by boat upstream or downstream may be asked 

Tricks and Tips to Solving Boats and Streams Questions

Some important tricks and tips for solving boats and streams questions are:

  • The first step to solving the boats and streams problems is to thoroughly read the question with a calm mind. This helps understand the various terms behind the boats and stream concepts being applied.
  • If upstream and downstream are not mentioned, do not be confused. You should remember that motion opposite to the flow of the stream is upstream and motion along the flow of the stream is downstream.
  • Do not forget to memorise the formulas related to boat and stream problems. Regularly going through the formulas will help memorise them. Knowing the exact formula required for a particular question helps solve the question easily.
  • The last, but not the least, a tip is constant practice. You will be able to solve the questions easily if you have been in practice.