It takes Ashley 8 hours to kayak 18 km up river and 18 km back down the river. if the river is flowing at 3 km/h, how fast did she puddle assuming she paddled at a constant speed?

Answer 1

her speed = v
current speed = 3

time up = 18/(v-3)
time down = 18/(v+3)
so
18[ 1/(v-3) + 1/(v+3) ] = 8

[ 1/(v-3) + 1/(v+3) ] = 4/9

[ v + 3 + v - 3 ] = (4/9)(v^2-9)

18 v = 4 v^2 - 36

2 v^2 - 9 v - 18 = 0

v = 6 for positive v root
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check
up speed = 3
down speed = 9
up time = 18/3 = 6
down time = 18/9 = 2
total = 8 hr ok