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**Upstream**: It means that you are moving in opposite direction from that in which river flows.**Downstream**: It means moving along in the direction of the flow of the stream.

Let the speed of boat be **a km/hr**. and speed of the stream be **b km/ hr. **Therefore, the relative speed of boat going upstream is (**a-b**) km/hr. and speed of the boat going downstream will be (**a + b**) km/hr.**Still water**: When the water is still and not moving and there’s no flow like that in case of ponds then it’s called still water.

Then, the relative speed of boat in still water is ½ (**a + b**) km/hr. And, the speed of stream is ½ (**a – b**) km/hr.

**Some basic types of questions asked in exam**

• Time based questions

• Speed based questions

• Average speed-based questions

• Distance based questions

Now let’s learn some problem-solving in above mentioned questions:

**1. Time based question: **In this kind, you will be given speed of the boat and stream in still water. You need to calculate the time to go upstream/ downstream. There can also be other questions in calculation of time and some of them can be easily be solved using the formulas given below.

**Example 1:** The speed of a motor boat is that of the stream as 36:5. The boat goes along with the stream in 5 hours and 10 minutes. How much time will it take to come back.**Sol) **Let the speed of the motor boat and that of stream be 36x km/hr. and 5km/hr. respectively.

Then, the speed downstream = (36x + 5x) = 41km/hr.

Speed upstream = (36x – 5x) = 31 km/hr.

Let d the distance.

Then, d/41 km = 5 ^{10}/_{60} = ^{31}/_{6}

• d = 1271x/6

• Time taken while coming back = distance/speed = d/31x = 1271x/ (31x * 6) hrs. = 6 ^{5}/_{6}**2. Speed based question**: In this kind, you will be given speed of boat upstream and downstream, you need to find the speed of still water and stream.**Example 2:** The speed of the boat when traveling downstream is 32 km/hr. whereas when traveling upstream it is 28 km/hr. What is the speed of the boat in still water and the speed of the stream?**Sol) **This question requires direct use of the formula mentioned earlier.

Speed of the boat in still water = **½ (32 + 28) km/hr. = 30 km/hr**.

Speed of the stream = **½ (32 – 28) hm/hr. = 2 km/hr.**

Speed-based questions also include one more type in which time taken and distance covered is given along with speed of stream is given then you can find the speed of the boat in still water using following formula:

If a boat takes t^{}_{1} hours to complete distance downstream and t_{2} hours to complete the same distance upstream then,

**Speed of the boat in still water = b (t _{2} + t_{1})/ (t_{2} – t_{1}) km/hr.**

Speed of the boat in still water =

Upstream speed =

Boat’s speed in still water

Now we are in stage of using the average speed formula.

Average speed during whole journey =

There can be two different formulas to calculate the distance for two distant cases.

i.) If a boat takes t more hours in upstream then to travel downstream for the same distance when speed of still water is

Therefore, Width of the river =

ii.) If a boat takes t hours to row to a place and return back, then the distance between the two places can be estimated through

The above examples are just few simple and basic application of the methods stated along with them. These formulas can come in handy and can save lot of your time in exam. You can find questions and problems involving simultaneous use of more than one formula at times. But if you know the correct utilization of them you can solve any problem easily. And, this smoothness comes with practice so the more you varied questions you try the more you will learn and become better at solving them. So, keep practicing!

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