<PRE><B>Question 217462</B>
Jens boat cruised 45 miles upstream and 45 miles back in a total of 8 hr.
The speed of the river is 3 mph. 
Find the speed of the boat in still water.
:
Let s = speed in still water
then
(s+3) = speed downstream
and
(s-3) = speed upstream
:
write a time equation: Time = {{{dist/speed}}} 
:
Time up + time down = 8 hrs
{{{45/((s+3))}}} + {{{45/((s-3))}}} = 8
Multiply equation by (s-3)(s+3), results
45(s-3) + 45(s+3) = 8(s+3)(s-3)
:
45s - 135 + 45s + 135 = 8(s^2 - 9)
:
90s = 8s^2 - 72
:
8s^2 - 90s - 72 = 0; a quadratic equation
:
Simplify, divide by 2
4s^2 - 45s - 36 = 0
:
Factor
(4s + 3)(s - 12) = 0
:
Positive solution:
s = 12 mph boat speed in still water
;
;
Check solution:
{{{45/15}}} + {{{45/9}}} = 8
3 + 5 = 8 hrs</PRE>