Answer:
14hrs
Step-by-step explanation:
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
