On a hot and sunny summer day, Lena decides to take a trip with her boat. It takes 5 hours for her to row her boat down the river. If she continues to row at the same pace, she will need 6 hours to row back up the river. Now imagine that Lena is traveling the same distance with her boat on a lake (without a current).
How long would she be on the water if her boat traveled at a constant speed?
It is a uniform motion, so the following physical relationship is valid:
Speed x time = distance or s ∙ t = d
The time “t” is calculated accordingly: t = d/s
For our example this means:
5 = d/(S + s) → 5(S + s) = d, and
6 = d/(S - s) → 6(S - s) = d
Where “S” the speed of the boat and “s” is the speed of the current.
By setting the two equal to one another, you get:
5(S + s) = 6(S - s)
5S + 5s = 6S - 6s
11s = S
So, the speed of the boat is eleven times greater than the speed of the current.
t = d/s and the distance “d” can be calculated using
d 5(S + s) = 6(S - s),
which yields d = 5 [ S + (1/11)S ] = 6 [ S - (1/11)S ] = (60/11)S
t = d/s = 60/11
Because you have to consider the distance there and back, the result is:
t = 120/11 = 10 (10/11)h = 10h 54,5 seconds
It is logical that a trip without a current is shorter, because traveling with the current is shorter than traveling against the current.