Question 80784
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?
:
Let s = speed of the boat in still water
Then:
(s-3) = speed up-river
and
(s+3) = speed down-river
:
Write a time equation: Time = distance/speed
:
Time up-river + Time down-river = 9 hrs
{{{60/(s-3)}}} + {{{60/(s+3)}}} = 9
;
Multiply equation by (s+3)(s-3) and you have:
:
60(s+3) + 60(s-3) = 9(s+3)(s-3)
:
60s + 180 + 60s - 180 = 9(s^2 - 9)
:
120s = 9s^2 - 81
:
9s^2 - 120s - 81 = 0; a quadratic equation
:
Use the quadratic equation to find s: a=9; b=-120; c=-81
:
{{{s = (-(-120) +- sqrt(-120^2 - 4*9*-81 ))/(2*9) }}}
:
{{{s = (+120 +- sqrt(14400 + 2916 ))/(18) }}}
:
Do the math, you should get a positive solution of:
:
s = 13.977 mph, speed in still water
:
:
Check on calc, find the times at each speed:
60/16.977 + 60/10.977 = 9.00 hrs