SOLUTION: a boat takes 2 hours longer to go 45 miles up a river than to return. If the boat's speed in still water is 12 mph, what is the rate of the current. Can you please show you step t

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Downstream Data: distance= 45; rate=12+c; time=45/(12+c)
Upstream Data: distance = 45: rate = 12-c; time= 45/(12-c)
EQUATION:
Time Upstream - Time Downstream = 2 hours
45/(12-c) - 45/(12+c) = 2
Divide thru by 45 to get:
1/(12-c) - 1/(12-c) =2/45
Simplify :
45[(12+c)-(12-c)]= 2[(12-c)(12+c)]
45[2c] =2[144-c^2]
90c = 288-2c^2
c^2+45c-144=0
(c-3)(c+48)=0
current speed = 3 mph
Cheers,
Stan H.