# algebra

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A canoeist can paddle 12 km upstream and 12 km back downstream in the same amount of time as she can paddle 25 km in still water. If the rate of the current is 2 km/hour, what is her rate in still water?

• algebra -

Let her rate in still water be x km/h

time in still water = 25/x hours

time to go upstream = 12/(x-2)
time to go downstream = 12/(x+2)

12/(x-2) + 12/(x+2) = 25/x

(12x + 24 + 12x - 24)/(x^2 - 4) = 25/x
24x/(x^2 - 4) = 25/x
25x^2 - 100 = 24x^2
x^2 = 100
x = ± √10

rate in still water is 10 km/h

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