Arturo O. answered • 05/28/16

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v = speed in still water

t = downstream trip time

d = distance = 182 miles; same distance both downstream and upstream

t + 12 = upstream return trip time

u = current flow = 3 mph

Downstream: d = (v + u)t; Upstream: d = (v - u)(t + 12)

(v - 3)(t + 12) = 182 (equation 1)

(v + 3)t = 182 (equation 2)

Subtract equation 2 from equation 1 to get t:

(vt + 12v -3t -36) - (vt + 3t) = 0

12v - 6t - 36 = 0

t = 2v - 6

Substitute this result for t into equation 2 and solve for v:

(v + 3)(2v - 6) = 182

2v^2 - 6v + 6v - 18 = 182

v^2 = 100

v = 10 mph

t = 2v - 6 = [2(10) - 6] hrs = 14 hrs