SOLUTION: The current of a river is 2 miles per hour. A boat travels to a point 8 miles upstream and back again in a Total of 3 hours. What is the speed of the boat in still water?

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Question 195406: The current of a river is 2 miles per hour. A boat travels to a point 8 miles upstream and back again in a Total of 3 hours. What is the speed of the boat in still water?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
The current of a river is 2 miles per hour. A boat travels to a point 8 miles
upstream and back again in a Total of 3 hours. What is the speed of the boat in still water?
:
Let s = speed of the boat in still water
then
(s+2) = speed downstream
and
(s-2) = speed upstream
:
Write time equation; Time = dist%2Fspeed
:
Time upstream + time downstream = 3 hrs
8%2F%28%28s-2%29%29 + 8%2F%28%28s%2B2%29%29 = 3
:
Multiply equation by (s-2)(s+2) to get rid of the denominator, results:
:
8(s+2) = 8(s-2) = 3(s-2)(s+2)
:
8s + 16 + 8s - 16 = 3(s^2 - 4)
:
16s = 3s^2 - 12
:
0 = 3s^2 - 16s - 12; a quadratic equation
:
Factors to:
(3s + 2)(s - 6) = 0
:
The positive solution is what we want here
s = 6 mph, speed in still water
:
:
Check solution using the time equation:
8/4 + 8/8 = 3