# Boat and Stream Concept, Formula, Questions

## Boat and Stream Concept, Formula, Questions

The concept of boat and a stream is one of the most popular themes on which questions are posed in the numerous government exams.

The boat and stream problems appear in the quantitative aptitude section of government exams, and their weightage varies from 1-3 marks.

To have a better knowledge of the topic, we will explore the boat and stream concept for answering questions, significant formulas, and some sample questions in this post.

Knowledge of all relevant Boat and stream concepts, Formula and questions, is vitally important for any competitive exam candidate who wishes to pursue a job career in the government sector.

### Important Terms

Stream – The moving water in a river is called a stream.

Upstream – If the boat is flowing in the opposite direction to the stream, it is called upstream. In this case, the net speed of the boat is called the upstream speed.

Downstream – If the boat is flowing along the direction of the stream, it is called downstream. In this case, the net speed of the boat is called downstream speed.

Still Water – Under this circumstance the water is considered to be stationary and the speed of the water is zero

Speed of boat – It is the speed of the boat in still water

Speed of Current/Stream – It is the speed of the river or we can say the rate at which the river is flowing.

### Upstream and Downstream Formula

Let “u” is the speed of the boat in still water and “v” is the speed of the Stream.

In upstream case, when boat is rowing against the water stream. In this case the effective speed of the boat is “u – v” , as the stream of water is against the boat.

In Downstream case, when boat is rowing with the water stream. In this case the effective speed of the boat is “u + v” , as the stream of water is with the boat.

Upstream Speed = Speed of Boat – Speed of Stream

Upstream Speed = (u−v)

Downstream Speed = Speed of Boat + Speed of Stream

Downstream Speed = (u+v)

Question 1. A boat can travel with a speed of 12 km/hr in still water. If the speed of the stream is 4 km/hr, find the time taken by the boat to go 48 km downstream.

Answer.  Here, Downstream speed = u + v = 12 + 4 = 16 Km/hr

Time taken to travel 48 km = Distance / Speed = 48 / 16 = 3 hr

Question. The speed of a boat in still water in 15 km/hr and the rate of current is 3 km/hr. The distance travelled upstream in 9 hour is ?

Answer. Here, Upstream speed = u – v = 15 – 3 = 12 km/hr

Distance covered in 9 hour

= Speed x Time = 12 x 9 = 108 km

Let’s denote downstream Speed with ‘a’ and Upstream speed with ‘b’

Downstream =>  a = (u+v) ……..(i)
Upstream     =>  b = (u−v)……..(ii)

Adding equation (i) and (ii), we get
a + b = u + v + u – v
a + b = 2u
u = (a + b) / 2

Subtracting equation (ii) from (i) , we get
u + v – ( u – v) = a – b
u + v – u + v = a – b
2v = a – b
v = (a – b)  / 2

Questions 2. A man rows downstream 32 km and 14 km upstream. If he takes 6 hours to cover each distance, then the velocity (in kmph) of the current is ?

Answer. Upstream Speed = 14/6 = b

Downstream Speed = 32/6 = a

Questions 3. If a man goes 18 km downstream in 4 hours and returns against the stream in 12 hours, then the speed of the stream in km/hr is ?

Answer. Speed Downstream = 18/4 = 4.5 km/hr
Speed Upstream = 18/12 = 1.5 km/hr
Speed of Stream = ½ ( 4.5 – 1.5 ) = 3/2 = 1.5 km/hr

Questions 4. A man can row at 5 kmph in still water. If the velocity of current is 1 kmph and it takes him 1 hour to row to a place and come back, how far is the place?

Answer. Speed downstream = 5 + 1 = 6 kmph

Speed Upstream = 5 – 1 = 4 kmph

Let the required distance is D km

Time (upstream ) + time ( downstream ) = 1 hr

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