Question

A swimmer can swim at a velocity v in still water. She swims upstream a distance d against the current, which has a velocity u. She then swims back to her starting point. A) how long does it take her to make the round-trip? B) what is her average speed for the trip? C) for what value of u u is her average speed the greatest?

Answer 1

Upstream speed: v - u
Downstream speed: v + u
Total distance: 2d

A) total time = d / (v - u) + d / (v + u)

B) Average speed = total distance / total time
V(av) = 2d / [ d / (v - u) + d / (v + u) ]
V(av) = 2d / [d(v + u + v - u) / (v - u)(v + u) ]
V(av) = (v² - u²) / v

C) If u is 0, her average speed will be the greatest, equal to v