Boats and Streams

Downstream/Upstream:
In water, the direction along the stream is called downstream. And, the direction against the stream is called upstream.

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 downstream = (u + v) km/hr.
Speed 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 (a + b) km/hr. 2 Rate of stream = 1 (a  b) km/hr. 2
TIP on cracking Aptitude Questions on Boats and Streams
Tip: Understand that the water current can help (when downstream) or hinder (when upstream) the boat
If Sb, Sc, Su and Sd be the speeds of the boat in still water, speed of the current in the stream, speed of the boat while running upstream and speed of the boat while running downstream respectively, then
Sb + Sc = Sd and Sb – Sc = Su
Question: A boat running upstream takes 8 hours 48 minutes to cover a certain distance, while it takes 4 hours to cover the same distance running downstream. What is the ratio between the speed of the boat and speed of the water current respectively?
Solution:
Let the distance travelled be ‘d’ meters
Sb – Sc = d/ 528 meters/ min [When travelling upstream]
Sb + Sc = d/240 meters/ min [When travelling downstream]
Solving the equations above, we get
Sb: Ss = 8: 3