Boats and Streams Question Solution Simplified – Solve in 1 Minute – codewindow.in

/ Aptitude / By Coder_Shark

Various competitive examinations ask questions regularly based on Boats and Streams. Many students face challenges in understanding and solving Boats and Stream problems.
Mainly we face challenges to solve Boat and Stream problems, as we never experienced much in a boat traveling or rowing with/against the flow of water etc. Therefore we get confused when we see terms like downstream, upstream, Speed of stream/current, still water, etc.
Let us take a real-life example and will try to understand Boats and streams. Once you understand the concept clearly you need not take much effort to remember the formula and even if you forget it during the exam, with help of a known concept you can generate the formula as and when required.

Real-life example to understand the concept of Boats and Streams:

Consider you have enrolled for 1 of the marathon for 1st time. Marathon means you need to complete 42km running. As you are participating for 1st time in the marathon, you started doing practice in one of the playgrounds nearby your home.
The playground is a completely plain surface without any upward or downward slope in it. After practicing for a couple of months you achieved a speed of running on this plain play-ground of 10 km/hr.

On Marathon day, you saw the Marathon track:
1st half: Start from Point A and reach Point B [21 Km slope downwards]
2nd half: Same route return from point B to Point A [21 km slope upwards]

As you see in the image, 1st half there is a complete slope downwards. So obviously you get some boost for your speed and let us assume that boost is 5km/hr.
While returning whatever extra boost you got in 1st half is reduced as you were coming upwards of the slope and naturally your speed would reduce by 5 km/hr.
Let us summarize in terms of Boats and Stream:

So Downstream speed will always be greater than Upstream speed. Let us look at formulae and different types of problems.

Observe this table and respective values carefully and we can get the below formulae:
1) Speed at Downstream = Speed in Still water + Speed of Stream
2) Speed at Upstream = Speed in Still water – Speed of Stream
3) Speed in Still water = (Downstream Speed + Upstream Speed) / 2
4) Speed of stream = (Downstream Speed – Upstream Speed) / 2
5) Speed = Distance / Time and Time = Distance / Speed

Type 1:

Question 1:

Speed of boat in still water is 20 km/hr and rate of stream is 4 km/hr. What is speed of boat during downstream and upstream?

Solution:

Speed in still water = 20 km/hr
Speed of stream = 4 km/hr
Downstream speed = ?
Upstream speed = ?
Formula:
Speed at Downstream = Speed in Still water + Speed of Stream
= 20 + 4
= 24 km/hr

Speed at Upstream = Speed in Still water – Speed of Stream
= 20 – 4
= 16 km/hr

The answer is Speed at Downstream is 24 km/hr and speed at upstream is 16 km/hr.

Question 2:

The speed of a boat in still water is 15 km/hr and the speed of the stream is 1.5 km/hr. What is the speed of the boat during downstream and upstream?

Solution:

Speed in still water = 15 km/hr
Speed of stream = 1.5 km/hr
Downstream speed = ?
Upstream speed = ?
Formula:
Speed at Downstream = Speed in Still water + Speed of Stream
= 15 + 1.5
= 16.5 km/hr

Speed at Upstream = Speed in Still water – Speed of Stream
= 15 – 1.5
= 13.5 km/hr

The answer is Speed at Downstream is 16.5 km/hr and speed at upstream is 13.5 km/hr.

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Type 2:

Question 1:

Speed of boat at Upstream is 7 km/hr and speed of boat at downstream is 10 km/hr. Find speed of boat in still water and rate of stream.

Solution:

Speed at Upstream = 7 km/hr
Speed at Downstream = 10 km/hr
Speed in still water = ?
Speed of stream = ?
Formula:
Speed in Still water
= (Downstream Speed + Upstream Speed) / 2
= (10 + 7) / 2 = 8.5 km/hr
Speed of stream
= (Downstream Speed – Upstream Speed) / 2
= (10 – 7) / 2 = 1.5 km/hr

The answer is Speed in still water is 8.5 km/hr and Speed of stream is 1.5 km/hr.

Question 2:

In one hour, a boat goes 11 km along the stream and 5 km against the stream. Find the speed of the boat in still water and the rate of the stream.

Solution:

Speed at Upstream [against stream] = 5 km/hr
Speed at Downstream [along stream] = 11 km/hr
Speed in still water = ?
Speed of stream= ?
Formula:
Speed in Still water
= (Downstream Speed + Upstream Speed) / 2
= (11 + 5) / 2 = 8 km/hr
Speed of stream
= (Downstream Speed – Upstream Speed) / 2
= (11 – 5) / 2 = 3 km/hr

The answer is Speed in still water is 8 km/hr and the speed of the stream is 3 km/hr.

Question 3:

A man can row upstream at 8 km/hr and downstream at 13km/hr. Find the speed of the boat in still water and the rate of the stream.

Solution:

Speed at Upstream = 8 km/hr
Speed at Downstream = 13 km/hr
Speed in still water = ?
Speed of stream= ?
Formula:
Speed in Still water
= (Downstream Speed + Upstream Speed) / 2
= (13 + 8) / 2 = 10.5 km/hr
Speed of stream
= (Downstream Speed – Upstream Speed) / 2
= (13 – 8) / 2 = 2.5 km/hr

The answer is Speed in still water is 10.5 km/hr and the speed of the stream is 2.5 km/hr.

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Type 3:

Question 1:

A man takes 3 hours 45 minutes to row a boat 15 km downstream of the river and 2 hours and 30 minutes to cover 5 km upstream. Find the speed of the river current in km/hr.

Solution:

1 hour is 60 minutes so divide by 60 whenever time is given in minutes
Time taken to go 15 km downstream = 3 hours 45 minutes = 15/4 hours
Time taken to go 5 km Upstream = 2 hours 30 minutes = 5/2 hours
Speed of river current = ?
We need to find downstream and upstream speed first to identify speed of river current.
Formula:
Speed = Distance / Time
For Downstream speed = 15 / (15/4) = 4 km/hr
For Upstream speed = 5 / (5/2) = 2 km/hr
Now we have Upstream and downstream speed both available so we can easily find out speed of current
Speed of stream = (Downstream Speed – Upstream Speed) / 2
Speed of stream = (4 – 2) / 2 = 1 km/hr

Answer is speed of river Current is 1 km/hr.

Question 2:

A man rows downstream 32 km and 14 km upstream. If he takes 6 hours to cover each distance, what velocity (speed) of current is?

Solution:

Time taken to go 32 km downstream = 6 hours
Time taken to go 14 km Upstream = 6 hours
Speed of river current = ?
We need to find downstream and upstream speed first to identify speed of river current.
Formula:
Speed = Distance / Time
For Downstream speed = 32 / 6 = 16/3 km/hr
For Upstream speed = 14 / 6 = 7/3 km/hr
Now we have Upstream and downstream speed both available so we can easily find out speed of current
Speed of stream = (Downstream Speed – Upstream Speed) / 2
Speed of stream = (16/3 – 7/3) / 2 = (9/3)/2 = 1.5 km/hr

Answer is Speed of Stream is 1.5 km/hr.

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Question 3:

A motorboat covers a certain distance downstream in 1 hour, while it comes back in 1(1/2) hours. If the speed of the stream is 3 km/hr, what is the speed of the boat in still water?

Solution:

Let us assume speed in still water x km/hr.
Downstream speed = Speed in still water + speed of current = (x + 3) km/hr
Upstream speed = Speed in still water – speed of current = (x -3 ) km/hr
Distance is constant during upstream and downstream.
Downstream 1 hr distance = Upstream 1.5 hr distance
Distance = Speed * time
During downstream distance: (x + 3) * 1 = x + 3
During upstream distance = (x – 3) * 3/2
We need to solve below to get answer
x + 3 = (x – 3) * 3/2
x + 3 = (3x – 9)/2
2x + 6 = 3x – 9
x = 6 + 9 =15

Answer is speed in still water is 15 km/hr.

Type 4:

Question 1:

A motorboat whose speed is 15 km/hr in still water goes 30 km downstream and comes back in total 4 hours 30 minutes. The speed of stream in km/hr is?

Solution:

Speed in still water = 15 km/hr
Downstream 30 km + Upstream 30 km Time = 4 hours 30 minutes = 9/2 hours
Speed of stream = ?
Let us assume speed of stream x
Downstream speed = Speed in still water + Speed of current = (15 + x) km/hr
Upstream speed = Speed in still water – Speed of current = (15 – x) km/hr
Formula:
Time = Distance / Speed
Downstream Time = 30 / (15 + x)
Upstream Time = 30 / (15 – x)
30 / (15 + x) + 30 / (15 – x) = 9/2
(450 – 30x + 450 + 30x) / (225 – x^2) = 9/2
900 / (225 – x^2) = 9/2
1800 = 2025 – 9(x^2)
9(x^2) = 225
x^2 = 25
x = 5

Answer is speed of stream is 5 km/hr.

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Question 2:

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

Solution:

Speed in still water = 5 km/hr
Speed of current = 1 km/hr
Man rows to some place and returns back in 1 hour.
First we calculate speed of Downstream and upstream:
Downstream speed = Speed in still water + speed of current
= 5 + 1 = 6 km/hr
Upstream speed = Speed in still water + speed of current
= 5 – 1 = 4 km/hr
Let us assume total distance is 2x means x distance downstream and x distance back.
Time = Distance / Speed
Downstream Time = x/6
Upstream Time = x/4
x/6 + x/4 = 1
(4x+6x)/24 = 1
10x = 24
x = 2.4 km

Answer is place is 2.4 km far.

Question 3:

A man can row 7(1/2) km/hr in still water. If the river running at 1.5 km/hr, it takes him 50 minutes to row to a place and back, how far off is the place?

Solution:

Speed in still water = 7(1/2) km/hr = 7.5 km/hr
Speed of current = 1.5 km/hr
As person going and coming back in 50 minutes:
Downstream + Upstream time = 50 minutes = 50/60 hours = 5/6 hours
Downstream speed = speed in still water + Speed of current
= 7.5 + 1.5
= 9 km/hr
Upstream speed = speed in still water – Speed of current
= 7.5 – 1.5
= 6 km/hr
Let us assume total distance is 2x means x distance downstream and x distance back.
Time = Distance / Speed
Downstream Time = x/9
Upstream Time = x/6
x/9 + x/6 = 5/6
(6x + 9x)/54 = 5/6
15x/54 = 5/6
90x = 270
x = 3

Answer is distance is at 3 km far.

Question 4:

In stream running at 2 km/hr, the motorboat goes 6 km upstream and back again to starting point 33 minutes. Find the speed of the motorboat in still water.

Solution:

Speed of stream = 2 km/hr
Upstream + Downstream time = 33 minutes = 33/60 = 11/20 hours
1 side distance is 6 km.
Let us assume speed in still water x km/hr
Downstream speed = speed in still water + Speed of current
= x + 2
Upstream speed = speed in still water – Speed of current
= x -2
Time = Distance / Speed
Upstream Time = 6/(x-2)
Downstream Time = 6/(x+2)
6/(x-2) + 6/(x+2) = 11/20
(6x + 12 + 6x – 12)/(x^2 – 4) = 11/20
12x/(x^2 – 4) = 11/20
240x = 11(x^2) – 44
11(x^2) – 240x – 44 = 0
11(x^2) – 242x + 2x – 44 = 0
(x-22)(11x + 2) = 0
x = 22

Answer is Speed of boat is 22 km/hr.

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