Downstream: In water, the direction along the stream is called downstream.
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
Upstream: In water, the direction against the stream is called upstream.
Speed upstream = (u – v) km/hr
Now, suppose if the speed downstream is already given as x km/hr and the speed upstream is given as y km/hr, then
Speed in still water = (x + y) / 2 km/hr
Speed of the stream = (x − y) / 2 km/hr
Suppose a man swims at the speed of x km/hr in still water and he swims the same distance up and down in a stream which flows at a rate of y km/hr.
Then his average speed throughout the journey = (Speed downstream × Speed upstream) / (Speed in still water) = (x+y) * (x−y) / x
Solve the following question –
A man rows 135 km upstream in 2.7 hours. He rows the same distance downstream in 2.5 hours. However for downstream, he reduces his speed by 9%, while speed of the current gets reduced by 20%.
Find the Speed of the man.
img credit: BBC