The water of a stream keeps flowing at a constant speed in a particular direction. This is called the **speed of the stream** or current or water.

The speed with which a boat travels when there is no stream is called **speed of boat in still water**.

A boat can travel in the direction of current as well as against the current.

Basically 4 variables exist in these kinds of questions:

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Some of these variables are given in the question, rest others you have to find out. Sometimes speed is not given directly but given in terms of distance and time. In that case you can easily find out the speed by simple formula: **speed = distance/time**

I would suggest you to pick the variable name as per the name of variable e.g. I have used the variables b, w, u, d rather than simply using a, b, c, d.

This is just for the sake of convenience. If you use variable in such manner, you need not to waste time in knowing which variable represent which value when you get the values in the last. In objective type questions only one of these values is asked, so you can quickly pick which is the desired value. It makes your decision making faster and reduce the probability of error.

When boat travels against the stream, then boat is said to be travelling upstream. Obviously when boat is travelling against the stream, its effective speed will be reduced.

u = b – w --------- equation (1)

That means, if a boat is travelling against the stream then speed of boat in still water (b) must be higher that speed of stream (w). If b is not greater than w, then effectively boat will travel in the direction of stream.

When boat travels in the direction of stream, then obviously stream makes the effective speed of boat faster.

d = b + w --------- equation (2)

Let’s write the two equations discussed above again.

u = b – w --------- equation (1)

d = b + w --------- equation (2)

Hope its clear from the above two equations if the Downstream and Upstream speed of boat are given, we can easily find out value of rest two variable i.e. speed of boat in still water and speed of water. Let’s see how.

By adding equation (1) & (2):

b= (u+d)/2 --------- equation (3)

i.e. **Speed of boat in still water = (Upstream speed + Downstream speed)/2**

By subtracting equation (1) & (2):

w= (d-u)/2 --------- equation (4)

i.e. **Speed of water = (Downstream speed - Upstream speed)/2**

Lets summarize, all four equation as following way:

u = b – w

d = b + w

b= (u+d)/2

w= (d-u)/2

You need not to memorize these equations standalone. If you understand the concept, how these equations are derived, it is very easy to solve these kind of questions.

Happy Learning!