<PRE><B>Question 571335</B>
a boat traveled 135 mules downstream and back.
 The trip downstream took 5 hours and the return trip took 9 hours.
 If the speed of the current is 6 mph, what is the speed of the boat in still water?
:
Let s = speed of the boat instill water
then
(s-6) = effective speed upstream
(s+6) = effective speed downstream
:
Write a time equation: time = dist/speed
:
Upstr time + downstr time = 9 hrs
{{{135/((s-6))}}} + {{{135/((s+6))}}} = 9
Multiply by (s-6)(s+6), results:
135(s+6) + 135(s-6) = 9(s+6)(s-6)
:
135s + 810 + 135s - 810 = 9(s^2-36)
270s = 9s^2 - 324
0 = 9s^2 - 270s - 324
Simplify, divide by 9
s^2 - 30s - 36 = 0
Solve this using the quadratic formula
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
In this equation; x=s; a=1; b=-30; c=-36
{{{s = (-(-30) +- sqrt(-30^2-4*1*-36 ))/(2*1) }}}
:
{{{s = (30 +- sqrt(900-(-144) ))/2 }}}
:
{{{s = (30 +- sqrt(1044))/2 }}}
Two solutions but only this one is reasonable
{{{s = (30 + 32.311)/2 }}}
s = {{{62.311/2}}}
s = 31.156 mph in still water
:
:
See if this checks out
135/37.156 = 3.63 hrs
135/25.156 = 5.37
-------------------
total time: 9.00 hrs
</PRE>