# Algebra

The current of a river moves at 3 miles per hour. It takes a boat 3 hours to travel 12 miles upstream, against the current, and return the same distance traveling downstream, with the current. What is the boats rate in still water?

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1. boat's speed in still water --- x mph
against the current ----- x-3 mph
with the current -------- x + 3 mph

time against current = 12/(x-3)
time with the current = 12/(x+3)

12/(x+3) + 12/(x-3) = 3
times (x-3)(x+3) or x^2 - 9
12(x-3) + 12(x+3) = 3(x^2 - 9)
12x-36 + 12x + 36 = 3x^2 - 27
3x^2 - 24x - 27 = 0
x^2 - 8x - 9 = 0
(x-9)(x+1) = 0
x = 9 or x = -1, I guess we'll reject that negative

the boat's speed in calm water is 9 mph

check:
12/12 + 12/6
= 1 + 2
= 3hrs.

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