# Boat and Stream

Boat and Stream is one of the essential topic for every competive exam. Many varieties of question can be asked from this topic.
The boat and Stream questions asked in the quantitative Aptitude section and mostly the weightage of the question is 1- 3 marks.

Let’s discuss the boat and Stream concept, formula, tips and shortcuts to solve the question and some example to better understanding the topic.

## Concept of Boat and Stream

To solving the question it is essential we know about the concept of topic because questions generally asked in the exam based on this concept.

• Stream – The moving water is called stream.
• Upstream – If the boat is following in the opposite direction to the Stream, It is called upstream.
• Downstream – If the boat following along the direction of the stream , It is called Downstream.
• Still Water – The water is considered to be stationary and the speed of the water is zero , It is called still water.

Note:-The net speed of the boat is called Downstream as well as Upstream.

## Formula

These are the few important formula , with the help of this formula you can solve boat and Stream problem very easily.

• Upstream – (u-v) km/hr. Where, “u” is the speed of the boat and “v ” is the speed of stream.
• Downstream – (u+v) km/hr. Where, “u” is the speed of the boat and “v” is the speed of stream.
• Speed of Boat in still water – 1/2 (Downstream speed + Upstream speed ).
• Speed of Stream – 1/2( Downstream speed – Upstream speed)
• Average speed of boat – upstream speed × downstream speed / boat speed on still water.
• Distance – {u^2 – v^2 ×t} / 2u
• Distance – {u^2- v^2 × t } / 2v
• Speed of man in still water – {v ×( t2 + t1)/ (t2- t1)km/hr.
• Distance between two place = {t × (x^2 – y^2)/ 2x}

## Types of questions :-

Problem 1 :
A boat is rowed down a river 28 km in 4 hour and up a river 12km in 6 hour.Find the speed of the boat and the River.

Solution:-
Downstream speed = 28/4 km / h = 7 km/h
Upstream Speed = 12/6 km/ h = 2 km/h

By using Formula,
Speed of the boat in river = Downstream + upstream / 2
= 7 + 2 / 2 = 9/ 2 = 4.5km/ h

Speed of stream = Downstream – upstream / 2

= 7 – 2/ 2 = 5/2 = 2.5 km/h

Problem 2 :-
A motor boat can move with a speed of 7km/ h.
If the river is flowing at 3km/ h. It takes him 14 hours for a round trip.Find the distance between two place ?

Solution :-

Given,
X = 7 ,Y= 3 and T = 14 Hours.
By using the formula,
Distance between two place = { 14 × ( 49 – 9 )/2× 7} = 14 × 40/ 14 = 40 km

Problem 3 :-
Find the average Speed of a boat in a round trip between two place 18 km apart. If the speed of the boat in still water is 9 km/h and the speed of the river is 3 km/h.

Solution:-
Average speed = Upstream speed × Downstream speed / boat speed of still water.
= 6× 12/ 9 = 8 km/h.

Problem 4 :-
A man can row upstream at 16 km/hr and downstream at 26 km/hr. What is the speed of the stream?

Solution:-
Given,
Upstream = 16 km/ h
Downstream = 26 km/ h

By using the formula,
Speed of the stream = 1/2 ( Downstream – Upstream)
= 1/2 ( 26 – 16) = 1/2 × 10 = 10/2 = 5 km/ hr.

Problem 5 :-
A boat is moving 2 km against the current of the stream in 1h and moves 1km in the direction of the current in 10 minutes. How long will it take the boat to go 5km in stationary water?

Solution:-

Downstream = 1/10 × 60 = 6km/h
Upstream = 2km/h

Speed in still water = 1/2 (6+4) = 4 km/ h

Time taken by the boats to go 5km in stationary water = 5/ 4 hours = 1/4 hours = 1 hr 15 minute.

Problem 6:-
A man can swim in water with speed of 13 km/ h in still water. If the speed of the stream is 4km/ h. What will be the time taken by the person to go 68 km downstream.

Solution :-
Downstream speed = 13 + 4 km/h = 17 km/ h
To travel 68 km downstream,
Time taken = 68/17 = 4 hours.

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