A man rows at 6 km/hr in still water and with the same effort he rows 4.5 km/hr against the stream of a river. What is the speed if he rows (with the same effort) along the stream of the river?
Speed of man in still water, v = 6 km/hr.
Speed against the stream (upstream speed) = Speed in still water – Speed of stream = v – u.
We are given that the speed against the stream is 4.5 km/hr.
v – u = 4.5
Substitute the value of v:
6 – u = 4.5
u = 6 – 4.5 = 1.5 km/hr.
The speed of the river stream is 1.5 km/hr.
We need to find the speed if he rows along the stream (downstream speed) with the same effort. The effort remaining the same means his speed relative to the water is still v.
Speed along the stream (downstream speed) = Speed in still water + Speed of stream = v + u.
Substitute the values of v and u:
Downstream speed = 6 + 1.5 = 7.5 km/hr.
The question asks for the speed in one of the given options. 7.5 km/hr is equivalent to 7 and a half km/hr.
7.5 = 7 + 0.5 = 7 + 1/2 = 7½ km/hr.
– Speed downstream = Speed in still water + Speed of stream.
– The effort remaining the same implies the speed of the man relative to the water (speed in still water) is constant.
Speed in still water = (Downstream speed + Upstream speed) / 2
Speed of stream = (Downstream speed – Upstream speed) / 2
In this case, we found v=6 and u=1.5.
Upstream speed = 6 – 1.5 = 4.5 km/hr (Given).
Downstream speed = 6 + 1.5 = 7.5 km/hr (Calculated).
Check using the formulas:
Speed in still water = (7.5 + 4.5) / 2 = 12 / 2 = 6 km/hr (Matches given v).
Speed of stream = (7.5 – 4.5) / 2 = 3 / 2 = 1.5 km/hr (Matches calculated u).