SOLUTION: The current of a river is 2 miles per hour. It takes a motorboat a total of 3 hours to travel 8 miles upstream and return 8 miles downstream. What is the speed of the boat in still

Question 363778: The current of a river is 2 miles per hour. It takes a motorboat a total of 3 hours to travel 8 miles upstream and return 8 miles downstream. What is the speed of the boat in still water?
Answer by amoresroy(361) (Show Source): You can put this solution on YOUR website!
Distance = Speed * Time
Let s = speed of motorboat in still water
t = distance / speed
8/(s+2) + 8/(s-2) = 3
Multiply both sides by (s+2) (s-2)
8 (s-2) + 8 (s+2) = 3(s+2) (s-2)
8s-16 + 8s+16 = 3 (s^2-4)
16S = 3s^2 -12

Subtract 16s from both sides
0 = 3s^2 -16s -12
= (3s+2) (s-6)
s-6 =0
S = 6
The speed of the motorboat is 6 miles per hour.

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