Boats and Streams

Anyone who has given competitive exams will know the weightage of boats and streams in their syllabus. Such a vital topic requires constant practice to solve any of its questions with confidence. The topic being simple, students often do it on the last day before their exam. Despite being simple, the major mistake that happens is when students don’t understand the question completely before answering. That’s the reason, if they get stuck, they panic and forget even those concepts that they are well-versed at. The article is concise enough to give you revision of boats and streams formula as well as a simple explanation on what is the average speed of stream and boat in still water along with other important terms regarding boats and streams.

Boats and Streams Formulas

• Speed = Distance/Time

• Upstream [Against the stream (U)]

As per the concept, U = B (Boat speed) – S (Stream speed)

• Downstream [Along the stream (V)]

As per the concept, V = B (Boat speed) + S (Stream speed)

• Boat Speed (B) [Speed in still water]

For boat speed, we need to consider both cases, 

U = B – S ….(1)

V = B + S ….(2)

On adding both the equations, we get

2B = U + V

B = (U+V)/2

• Stream speed (S) 

For stream speed, we need to consider both cases, 

U = B – S ….(1)

V = B + S ….(2)

On subtracting both the equations, we get

2S = U – V

S = (U-V)/2

• Equating Distance

As in both the cases for boats and streams formula, the distance covered by the boat is the same as other terms of speed and time differ.

D_u = D_v

As per the speed formula,

T_u × U = T_v × V

T_u (B – S_u ) = T_v(B + S_v)

• Average Speed of Stream and Boat in Still Water

In boats and streams formula equation form, average speed of boat can be written as, 

Average speed of boat = (Upstream speed × Downstream speed)/Boat speed in still water = (U × V)/B

• If a boat covers a similar distance by taking time ‘t’ for going upstreams and coming back downstream, its distance is written as

Distance = [(B² – S²)(t)] / 2S

• When a boat travels downstream in ‘t1’ time and covers the same distance upstream in ‘t 2’ time, then the speed of the boat in still water or boat speed is

B = S (t₂+t₁ )/(t₂-t₁ ) km/hr

Speed of the Stream

Boats and streams formulas give us an idea of how the speed of the boat is affected by the speed of the stream. The stream has a direction of flow. Depending on the direction of the boat, the speed of the boat is decided. As still water does not have any speed of its own, it is not considered. 

• Upstream (Against the stream) – Here, the boat is moving with a speed and is travelling against the stream, where the stream also has some speed. The boat is travelling against the stream; thus, its speed will reduce. Here, the directions of speed of the stream and the boat are against each other. This will cause a change in the time taken to cover the same distance in still water, i.e., in the absence of the speed from the stream, it will take more time to cover the distance. Thus, the speed of a stream can be measured with the help of boats and streams formula, 

U (Upstream) = B (Boat speed) – S (Stream speed)

• Downstream (Along the stream) – Here, the boat is moving at a speed and is travelling along the stream, where the stream also has some speed; thus, its speed will increase. The directions of speed of the stream and the boat are in one direction. This will cause a change in the time taken to cover the same distance in still water, i.e., in the absence of the speed from the stream, it will take less time to cover the distance. Thus, the speed of a stream can be measured with the help of boats and streams formula, 

V (Downstream) = B (Boat speed) + S (Stream speed)

In both cases, the distance covered by the boat is the same.

Conclusion

It is always advisable that we understand a concept before memorising it because we can decide which boats and streams formula to be used as per the question only when we understand these concepts. The more you revise and practice, the more you will be able to face complex questions of boats and streams. The core concept lies in the basic speed formula. Sometimes, a question is made to look complex, whereas it can be solved in a minute. However, for basic boats and streams formula concept, practising always has profited. Remember that the speed of the stream affects the speed of the boat and not vice versa.