The speed of river current is 1.25 miles per hour
Solution:
Given that speed of a kayaker is 5.75 mi/h paddling with the river current and 3.25 mi/h paddling against it
To find: speed of river current
In water, the direction along the stream is called downstream
And, the direction against the stream is called upstream
Therefore, from given statement,
Speed of downstream = 5.75 miles per hour
Speed of upstream = 3.25 miles per hour
Formula to be used:
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
Therefore, we get
5.75 miles per hour = u + v
u + v = 5.75 ----- eqn 1
3.25 miles per hour = u - v
u - v = 3.25 ----- eqn 2
Solve the above two equations
Add eqn 1 and eqn 2
u + v + u - v = 5.75 + 3.25
2u = 9
u = 4.5
Substitute u = 4.5 in eqn 1
4.5 + v = 5.75
v = 5.75 - 4.5
v = 1.25
Thus speed of river current is 1.25 miles per hour