SOLUTION: The Hudson River flows at a rate of 5 miles per hour. A patrol boat travels 40 miles upriver, and returns in a total time of 6 hours. What is the speed of the boat in still water

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Question 179410: The Hudson River flows at a rate of 5 miles per hour. A patrol boat travels 40 miles upriver, and returns in a total time of 6 hours. What is the speed of the boat in still water?
Answer by MissionPossible(18) About Me  (Show Source):
You can put this solution on YOUR website!
the speed of the boat in still water = V (mile/hour)
Time = T
distance(D) = V*T or T = D/V
upriver the speed would be V-5
downriver the speed would be V+5
T = D/V
upriver Tup = 40/(v-5)
donwriver Tdown = 40/(v+5)
Tup + Tdown = 6
40/(v-5) + 40/(v+5) = 6
[40(v+5) + 40(v-5)]/[(v+5)(v-5)] = 6
40V+ 200 + 40V -200 = 6[(v+5)(v-5)]
80V = 6 (V^2-25)
80V = 6V^2 - 150
0 = 6V^2 - 80V - 150
(6V+10)(V-15) = 0
V = -10/6 , 15 choose only the positive value (15)
Then V = 15 miles/hour
the speed of the boat in still water = 15 mile/hour