Boats and streams
General terms:
1) Still water: The water of a river or any other water body which is not flowing is known as still water.
2) Stream: It is the flowing water of a river which is moving at a certain speed.
3) Upstream: The boat or a swimmer moving against the stream is known as moving upstream i.e. against the flow of water.
4) Downstream: The boat or a swimmer moving along the stream is known as moving downstream i.e. along the flow of water.
Basic Formulas
=> If the speed of a boat in still water is u km/hr and the speed of the stream is v km/hr, then
*speed of boat in downstream = u+v km/hr
*speed of boat in upstream = u-v km/hr
=>if the speed downstream is a km/hr and the speed upstream is b km/hr, then
*speed in still water = [(1/2)* (a+b)] km/hr
*Rate of stream = (1/2) * (a-b) km/hr
Points to remember:
1) If the speed of the boat or swimmer is X km/hr and the speed of the stream is Y km/hr,
The speed of the boat or swimmer in the direction of the stream is known as speed downstream. It is given by;
Speed downstream= (X+Y) km/hr
And, the speed of the boat or swimmer against the stream is known as speed upstream. It is given by;
Speed upstream= (X-Y) km/hr
2) Speed of man or boat in still water is given by;
= (1/2) ( speed downstream + speed upstream)
3) Speed of the stream is given by;
= (1/2) ( speed downstream - speed upstream)
4) A man can row at a speed of X km/hr in still water. If the speed of the stream is Y km/hr and the man rows the same distance up and down the stream, his average speed for the entire journey is given by;
= (speed upstream * speed downstream) / speed of man in still water
= [(X-Y)* (X+Y)] /X km/hr
5) A man can row a boat in still water at X km/hr. If the stream is flowing at Y km/hr it takes him t hours more to row upstream than to row downstream to cover the same distance. The distance is given by;
Distance = (X^2 - Y^2)t/2Y km/hr
6) A man can swim in still water at X km/hr. If the stream is flowing at Y km/hr it takes him t hours to reach a place and return back to the starting point. The distance between the place and the starting point is given by;
Distance = (X^2 - Y^2)t/ 2X km/hr
= Y [(t2 + t1) / (t2 - t1)] km/hr
8) A boat or swimmer takes K times as long to move upstream as to move downstream to cover a certain distance. If the speed of the stream is Y km/hr, the speed of the boat or man in still water is given by;
= Y [(K +1) / (K-1)] km/hr
examples
1) The speed of a boat in still water is 5km/hr. If the speed of the boat against the stream is 3 km/hr, what is the speed of the stream?
A)1.5 km/hr
B)2 km/hr
C)2.5 km/hr
D)1 km/hr
The correct answer is B
explanation:
Let the speed of stream = X km/hr
Speed of boat = 5 km/hr
Speed upstream = 3km/hr
Speed upstream = speed of boat - speed of stream
∴ 3 = 5 - X
X = 5 - 3 = 2 km/hr
2) A man rows downstream at 20 km/hr and rows upstream at 15 km/hr. At what speed he can row in still water?
A)17.5 km/hr
B)18 km/hr
C)20.5 km/hr
D)22 km/hr
The correct answer is A
Speed in still water = (1/2)(speed downstream + speed upstream)
Speed downstream = 20 km/hr
Speed upstream = 15 km/hr
∴ Required speed = Apti Boat and streams 10 (20 + 15) km/hr
= Apti Boat and streams 11 ∗ 35 = 17.5 km/hr
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