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?
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
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