# Important Boats and Streams Formulas

1. When the boat goes against the current of the river is referred to as Upstream. In other words, the direction against the river current is called upstream.
If the speed of motorboat in still water is x km/hr and the speed of stream is y km/hr then Upstream Speed = (x - y) km/hr
2. When the boat goes with the current of the river is referred to as Downstream. In other words, the direction along the river current is called downstream.
If the speed of motorboat in still water is x km/hr and the speed of stream is y km/hr then Downstream Speed = (x + y) km/hr
3. In the question, you will be given downstream speed and upstream speed and asked for speed of a boat in still water and the speed of the current. In that case, use the below formula to get the answer-
Let downstream speed is a km/hr and upstream speed is b km/hr then,
Speed of boat in still water =
 a + b2

Speed of stream =
 a - b2

Trick 1
The speed of a boat in still water is x km/hr. If the river is flowing at a rate of y km/hr and the boat covers the same distance up and down in the river, then average speed of it is = (Upstream Speed x Downstream Speed) / Speed of boat in still water

Thus, we can see that the average speed does not depend on the distance between the two points.
Example- A man can row a boat in still water at 12 km/hr and speed of the current is 6 km/hr. Find the average speed if the distance between two points is 30 km?

Average speed = Upstream Speed x Downstream Speed / Speed of boat in still water
Average speed =
 18 x 612
= 9 km/hr

Trick 2
Boat's speed in still water is x km/hr and the speed of a stream is y km/hr. If the boat takes t hours more in going upstream than to go in downstream, then the distance between two places is
 t * ( x2 - y2 )2y

Example- Rohan is practicing for a swimming competition in a small river. His speed in swimming pool is 4 km/hr. He finds that the speed of the river is 1 km/hr. He took 16 min more to cover against the stream than downstream. What is the width of the river?
Width of the river =
 16(42 - 12)2x1

=
 16x1560x2

= 2 km