Boats and Streams is an essential topic for many competitive exams. Many varieties of questions can be framed from this area. We use the fundamental concepts of time speed and distance only to solve elementary questions on Boats and Streams.

However, some types of questions are tricky and take lots of time to solve by applying textbook approach. Fortunately, there are some shortcut formulas available to handle such problems.

In this web notes, besides an understanding of the basic concepts of boats and streams, we will also learn few tricks to solve some exceptional questions.

Stream: It implies that the water in the river is moving or flowing.

Downstream or with the stream: It indicates that the stream favors the man’s rowing (or boating). i.e., the direction of rowing and direction of flow (stream) is same.

Upstream or against the stream: It indicates that the stream flows against the man’s rowing (or boating), i.e., the direction of rowing and direction of the stream (current) are opposite.

Some shortcut formulas related to the speed of boats and streams is handy as we require them frequently. Below are the lists of the formulas:

A boat is said to go downstream if it is moving along the direction of the stream. The net speed of the boat in this case is called downstream speed.
A boat is said to go upstream if it is moving in the direction opposite to the direction of the stream. The net speed of the boat in this case is called upstream speed.
Let the speed of the boat in still water is 'b' km/hr and the speed of the stream is 'w' km/hr. When the boat goes downstream then the speed will be (b + w) km/hr as in this case the water will take the boat along with it.
When the boat goes upstream then the speed will be (b - w) km/hr as in this case the water will offer resistance to the boat.
Let the downstream speed = d = b + w ……….(i)
Then the upstream speed = u = b – w ………(ii)
Adding the two equations, we get 2b = d + u.
⇒ b = (d+u) / 2 which gives the speed of the boat in terms of downstream and upstream speed. Subtracting the equation (i) and (ii), we get d – u = 2w ⇒ w = (d-u) / 2 which gives the speed of the stream in terms of downstream and upstream speed. You should remember these boats and streams formulas.

eg - A man rows 18 km down a river in 4 hours with the stream and returns in 12 hours. Find his speed and also the speed of the stream.

Explanation:

Speed with the stream (Downstream)= 18/4 = 4.5 kmph.

Speed against the stream (Upstream) = 18/12 = 1.5 kmph.

Therefore, speed of the stream = 1/2(4.5 – 1.5) = 1.5 kmph and speed of the man = 4.5 – 1.5 = 3 kmph.