SOLUTION: The Hudson River flows at a rate of 3 miles per hour. A patrol boat travels 60 miles upriver, and returns in a total time of 9 hours. What is the speed of the boat in still water

Algebra ->  Human-and-algebraic-language -> SOLUTION: The Hudson River flows at a rate of 3 miles per hour. A patrol boat travels 60 miles upriver, and returns in a total time of 9 hours. What is the speed of the boat in still water      Log On


   

Question 144580: The Hudson River flows at a rate of 3 miles per hour. A patrol boat travels 60 miles upriver, and returns in a total time of 9 hours. What is the speed of the boat in still water?
Found 2 solutions by josmiceli, shahid:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let s= speed of the boat in still water
The current = 3 mi/hr
In words:
(distance traveled upriver)/(rate going upriver)
+ (distance traveled downriver)/(rate going downriver) = 9 hrs
60+%2F+%28s+-+3%29+%2B+60+%2F+%28s+%2B+3%29+=+9
multiply both sides by %28s+-+3%29%28s+%2B+3%29
60%2A%28s+%2B+3%29+%2B+60%2A%28s+-+3%29+=+9%28s%5E2+-+9%29
divide both sides by 3
20%2A%28s+%2B+3+%2B+s+-+3%29+=+3s%5E2+-+27
40s+=+3s%5E2+-+27
3s%5E2+-+40s+-+27+=+0
solve using quadratic fornula
s+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
s+=+%28-%28-40%29+%2B-+sqrt%28+%28-40%29%5E2-4%2A3%2A%28-27%29+%29%29%2F%282%2A3%29+
s+=+%2840+%2B-+sqrt%281600+%2B+324+%29%29+%2F+6+
s+=+%2840+%2B-+sqrt%281924+%29%29+%2F+6+
s+=+%2840+%2B+43.863%29%2F6
s+=+83.86%2F6
s+=+13.98mi/hr
If you plug this back into the original equation, it checks out

Answer by shahid(44) About Me  (Show Source):
You can put this solution on YOUR website!
let x mph be the speed of the boat in still water then
(x+3)mph will be the speed of boat downstream
(x-3)mph will be its speed in upstream
now time taken by baot upstream t1=60/(x-3) and time taken by boat in downnstream t2=60/(x+3)
t1+t2=9
60/(x-3)+60/(x+3)=9
60{1/(x-3)+1/(x+3)}=9
x+3+x-3/x^2-9=9/60 taking LCM and dividing by 60
2x/x^2-9=3/20
20(2x)=3(x^2-9)
40x=3x^2-18
3x^2-40x-18=0 solve this equation to get your answer