## Monday, December 3, 2018

In this article on Boats and Streams Basic To Advance Chapter 1, we are sharing some important formulae used in Boats and Streams with important questions which are usually asked in Quantitative Aptitude section of various competitive examinations. Once you have understood the basics of Boats and Streams, you can solve any problem from this topic in no time.

Here we will discuss various different types of questions on Boats and Streams and the easiest, quickest and simplest way to deal with them. Let us first start with some basic formulae used in Boats and Streams and then talk about this chapter where the questions are based on basic relationships between the different variables of boats and streams.

Boats and Streams problems are usually based on a boat flowing in the river or stream or current. If the boat is flowing along the stream or in the same direction of stream then it's called Downstream and if the boat is flowing against the stream then it's called Upstream. The questions on Boats and Streams consists of the relationship among speed of boat, speed of a stream or time taken by the boat to cover certain distance. Sometimes in questions boats are replaced by a person, but the formula and the method to solve the problems remains same.

Assuming,
Speed of the stream (or current) = S
Speed of Boat⛵in still water = B

Then,
Speed of Boat along the stream or downstream,
=> D = B + S

Speed of Boat against the stream or upstream,
=> U = B - S

From the above obtained downstream and upstream speed, we can also find speed of boat and speed of stream with the formula given below.

Speed of Boat,
=> B = (D+U)/2

Speed of Stream or Current,
=> S = (D-U)/2

Now let us start solving some basic examples based on Boats and Streams and then move towards some advance level questions.

Q.) A man can swim with the stream at 3 kmph and against the stream at 2 kmph. How long will it take for him to swim 7.5 km in still water ?

Solution :

Given,
Downstream speed = 3 kmph
Upstream speed = 2 kmph

So Speed of Man can be calculated as,
=> S = (D+U)/2
=> S = (3+2)/2
=> S = 5/2 = 2.5 kmph

Now time taken for man to swim 7.5 km in still water,

=> Time = Distance/Speed
=> Time = 7.5 km / 2.5 kmph
=> Time = 3 hours [ANS]

Hence, it will take 3 hours for man to swim 7.5 km in still water.

Q.) A man can row 9 km in 3 hours upstream or against the stream running at 2 kmph. How long would he take in rowing the same distance while travelling downstream ?

Solution : From the given details, we can first calculate the speed of upstream as follows.

U = 9 km/3 hours = 3 kmph

And also given,
Speed of stream => S = 2 kmph

But we know,
=> S = 1/2 (D - U)
Putting the given values
=> 2 = 1/2 (D - 3)
After solving,
=> D = 7 kmph

So time taken to row the same distance downstream will be,
=> Time = Distance / Downstream speed
=> Time = 9/7 hours [ANS]

Hence, it will take 9/7 hours for man to row 9 km down the stream.
Q.) A boat goes upstream for 3 hours and then downstream for the same time. If the speed of the current is 3.5 kmph then how far from its original position is the boat now ?

Solution : Let the speed of boat in still water be x

Upward Speed = x - 3.5
And distance when boat is traveling with upward speed,
=> Distance = 3 × (x - 3.5)

Next,
Downstream Speed = x + 3.5
And the distance when boat is traveling with downstream speed,
=> Distance = 3 × (x + 3.5)

Now the Total distance covered by Boat from the point it starts,
=> Downstream distance - Upstream distance
=> 3 (x+3.5) - 3(x-3.5)
=> 3x + 10.5 - 3x + 10.5
=> 21 km [ANS]

Alternative Method

This displacement of boat is happening because of the moving water or current. So we will not consider the speed of boat in still water, as it will cancel each other.

Hence, distance covered by boat from its starting point will be equal to

=> Speed of stream × total time taken to cover upstream and downstream distance

=> 3.5 × (3+3)
=> 3.5 × 6
=> 21 km [ANS]

This is because, if the boat was moving in still water for 3 hours upstream and 3 hours downstream. Then there would have been no displacement.

Q.) The ratio of speed of a boat in still water and speed of stream is 6:1. If the difference between the distance covered by boat in 2 hours upstream and in 2 hours downstream is 8 km, what is the speed of boat in still water ?

Solution : Let the speed of boat be 6n and speed of stream be n. Now the given ratio can be written as,

Ratio of speed of boat in still water and speed of stream = 6n : 1n

Then,
Downstream Speed = 6n+1n = 7n
Upstream Speed = 6n-1n = 5n

And as know,
Speed × Time = Distance

Now as given in the question, the difference between the distance covered by boat in 2 hours upstream and in 2 hours downstream is 8 km. So this relation can be formed as

=> (7n×2) - (5n×2) = 8
=> 14n - 10n = 8
=> 4n = 8
=> n = 2

So, speed of boat = 6n = 6 × 2 = 12 kmph [ANS]

Alternative method

Displacement of boat is happening because of the moving water or current. So we will not consider the speed of boat in still water, as it will cancel each other.

So, distance covered by boat will be equal to Speed of stream × total time taken

=> 8 km = Speed of Stream × (2+2) hours
=> 8 km = Speed of Stream × 4 hours
=> Speed of stream = 2 kmph

Now it's given,
Ratio of speed of boat to speed of stream = 6:1

So we can write it as,

6 --------> ?
1 --------> 2

After cross multiply,
? = 2×6 =12 kmph.

Hence speed of boat in still water is 12 kmph.

Q.) A boat goes 2 km upstream and 3 km downstream in 5 hours while if it goes 6 km downstream and 3 km upstream, the boat takes 8 hours. Find the speed of boat, when it is going upstream.

Solution : The best way to solve these types of question is by equation method.

So when a boat is going 2 km upstream and 3 km downstream in 5 hours, it can be written as

2 (U) + 3 (D) ---------> 5 hours            ......(i)

And when a boat goes 6 km downstream and 3 km upstream in 8 hours, it can be written as

3 (U) + 6 (D) ---------> 8 hours            ......(ii)

Now since we need to calculate, speed of boat, when it's going upstream. We will try to eliminate the variable 'D' from both the equations.

Therefore multiplying eqn (i) by 2, it can  be written as

4 (U) + 6 (D) ---------> 10 hours            .....(i)
3 (U) + 6 (D) --------->  8 hours            .....(ii)

Here on subtracting eqn (ii) from eqn (i), we get

1 (U) --------> 2 hours

Means, a boat travels 1 km upstream in 2 hours, so from this we can calculate the speed of upstream.

As we know,
Speed = Distance/Time

Hence speed of boat going upstream will be,
=> 1 km / 2 hours
=> 0.5 kmph [ANS]

That's all in this article, we will be publishing more articles on Boats and Streams with solved examples, so stay connected with us and in case if you have any doubt, feedback or suggestion then please feel free to comment below. Keep Sharing and Happy Learning.

Thank You !!