Easy Ways to Solve Boats and Streams Problems

Easy Ways to Solve Boats and Streams Problems

Now a days job seekers are preparing for the bank exams. In every competitive exam aptitude round is there. In that aptitude round, number of questions will be coming from the Boats and Streams topic. Applicants will get difficult to prepare this Bats and Streams concept and they left this topic also. Lakhs of candidates applies for these Bank exams every year. This year also massive numbers of applicants were applied for the many bank jobs. In bank jobs, number questions will be asked from Boats and Streams concepts. For that reason we are providing the Easy Ways to Solve Boats and Streams concepts with simple formulas and examples here. Interested applicants can download the following steps to solve Boats and Streams problems easily.

Boats and Streams

Details about Easy Ways to Solve Boats and Streams Problems with Example:

Step 1: Finding Speed of Boat Using Direct Formula (Boats and Streams)

In this type, you will be finding speed of boat in still water (i.e., when water is not flowing/running). You have to remember a very simple formula as shown below.

Speed of the boat in still water = ½ (Downstream speed + Upstream speed)
Here, downstream speed denotes the speed of the boat in the direction of the stream, and, upstream speed denotes the speed of the boat against the direction of the stream.

2 more basic formulas that will help you are given below boats and streams.
Downstream speed = Speed of boat in still water + Speed of stream
Upstream speed = Speed of boat in still water – Speed of stream

Let us see an example to understand this type.

Example:

A boat travels at 9 km/h along the stream and 6 km/h against the stream. Find the speed of the boat in still water.

Solution:
From the question, you can write down the below values.
Downstream speed of the boat = 9 km/h
Upstream speed of the boat = 6 km/h

You have to substitute the above values in the below formula.
Speed of the boat in still water = ½ (Downstream speed + Upstream speed)
= ½ (9 + 6)
=7.5 km/h

Step 2: Finding Speed of Stream Using Direct Formula (Boats and Streams)

This type is similar to type 1. But there is one difference. Here you have to find speed of stream and not the speed of the boat.
You have to use the below formula to find speed of stream.

Speed of stream = ½ ( Downstream speed – upstream speed)

Below is your example.

Example Question 2: A man rows downstream 30 km and upstream 12 km. If he takes 4 hours to cover each distance, then the velocity of the current is:

Solution:
In this question, downstream and upstream speeds are not given directly. Hence you have to calculate them first.

Step 1: Calculation of downstream speed
You know that the man rows 30 Km in 4 hours downstream
You know the familiar formula that Speed = Distance/Time
Therefore, Downstream speed = Distance travelled downstream / Time taken
= 30/4 Km/h
Downstream speed = Distance travelled in downstream / Time taken in Downstream travel
= 30/4 … value 1

Step 2: Calculation of upstream speed
you know that the man rows 12 Km in 4 hours upstream
So, Upstream speed = Distance travelled in upstream / Time taken
=12/4 value 2

Step 3: Calculation of speed of stream
you have to substitute values got in steps 1 and 2 in below formula to find the speed of the stream.
Speed of the stream = ½ (Downstream speed – upstream speed)
= ½ (30/4 – 12/4)
= ½(18/4)
= 2.25 km/h

Step 3: Using Mans Still Water Speed Calculate Boats and Streams Speed (Boats and Streams):

Example:

A man can row 9 km/h in still water. It takes him twice as long to row up as to row down the river. Find the rate of the stream.

Solution:
Step 1: Calculate upstream and downstream speeds.
Assume that the man’s speed in upstream be X km/h
from the question, you know that his downstream speed is twice of upstream speed.
Then, his downstream speed = 2X km/h
You know the formula that, Man’s speed in still water = ½ (Upstream speed + Downstream speed)
=1/2 (X + 2X)
= 3X/2

But, in question, the man’s speed in still water is given to be 9 km/h
Therefore, 3x/2 = 9
X = 6 km/h.
Based on our assumptions, you can easily calculate upstream and downstream speeds as shown below.
Upstream speed = X = 6 km/h
Downstream speed = 2X = 12 km/h

Step 2: Calculate Speed Of The Stream
You already know the basic formula shown below.
Speed of the stream = ½ (Downstream speed – Upstream speed)
If you substitute the downstream and upstream speeds of step 1 in the above formula, you will get,
Speed of the stream = ½(12 – 6)
= 3 km/h.

Step 4: Equations Based Boats and Stream Problems

Example:

Kavin can row 10 km upstream and 20 km downstream in 6 hours. Also, he can row 20 km upstream and 15 km downstream in 9 hours. Find the rate of the current and the speed of the man in still water.

Solution:
You have to make below assumptions to form equations.
Let the upstream speed be X km/h
And downstream speed be Y km/h.
Time for downstream travel + Time for upstream travel = Total Time for upstream and downstream travel

Using the familiar Speed = Distance / Time formula, the above equation can be simplified as shown below.
Distance travelled in downstream/ downstream speed + Distance travelled in upstream/upstream speed = Total Time for upstream and downstream travel
If you substitute the values in question in above equation, you will get the below 2 equations.
10/x + 20/y = 6 …equation 1
20/x + 15/y = 9 …equation 2

Assume that 1/x = u and 1/y = v, Now you rewrite the above equations as given below.
10u + 20v = 6 …equation 3
20u + 15v = 9 …equation 4
If you multiply equation 3 by 2, you will get, 20u + 40v = 12 …equation 5

If you subtract equation 4 from equation 5, you will get
By cancelling out u, we get, v = 3/25
If you substitute v = 3/25 in equation 3, you will get,
10u + 20(3/25) = 6
10u + 12/5 = 6
10u = 18/5
u = 9/25
From the values of u and v, you can find the downstream and upstream speeds as shown below.
Upstream speed = X = 1/u = 25/9 km
and Downstream speed = Y = 1/v = 25/3 km
you can now calculate the speed of the man in still water, using our familiar formula.
Speed of the man in still water = ½ (downstream speed + upstream speed)
= ½(25/3 + 25/9)
=½(100/9) = 50/9 = 5.6 kmph

Also, you know the formula for speed of the current.
Speed of the current = ½ (downstream speed – upward stream)
= ½(25/3 – 25/9)
=1/2(50/9) = 25/9 = 2.8 km/h

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