How fast will the boat go?

let b = speed of boat
downstream rate = b +4
downstream time = t hours
upstream rate = b - 4
upstream time = t + 1/3 hours

distance = rate * time
downstream: (b + 4)(t - 1/3) = 5
upstream: ..... (b - 4)t = 5 ======> t = 5/(b-4)

substitute value found t "upstream" equation in "downstream" equation, , solve:

(b + 4)( [5/(b-4)] - 1/3) = 5
(b + 4)( [15 - (b-4)] / [(3)(b-4)] ) = 5
(b + 4)( [19 - b] / [3b - 12] ) = 5
(b + 4)(19 - b) = 5(3b - 12)
19b - 4b - b² + 76 = 15b - 60
-19b + 4b + b² - 76 + 15b - 60 = 0
b² - 136 = 0
b² = 136
b = √136
b = 11.66 mph

debbie traveled boat 5 miles upstream fish in favorite spot. because of 4-mph current, took 20 minutes longer there return. how fast boat go in water?

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