# algebra

A motorvoat goes 36 miles upstream on a river whose current is running at 3 miles per hour. The trip up and back takes 5 hours. What is the speed of the boat ( assuming that it maintains a constant speed relative to the water)?

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1. t going upstream
(5 - t) going downstream

speed upstream = (v-3)
speed downstream = (v+3)

36 = t(v-3)
36 = (5-t)(v+3)

36 = t v - 3 t
t = 36/(v-3)

36 = [5 - 36/(v-3)] (v+3)
36 = 5(v+3) - 36(v+3)/(v-3)
(21 - 5 v)(v-3) = -36(v+3)

check, multiply out and solve quadratic for v

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