Question 1085997
Two boats travel in a river having a current of 5 km/hr.
 The boat going upstream had departed 1 hr before the boat going downstream.
 A period of time after the boat going downstream had departed, a radio conversation between the boats indicated that one boat was 44 km upstream and the other was 75 km downstream.
 Approximately, to the nearest tenth of a kilometer per hour, the speed of each boat. 
 Find the speed of the boats in still water. 
:
In order to do this problem you have to assume the boats have the same speed in still water
let s = the their still water speed
then
(s+5) = effective speed of boat1 going downstream
and
(s-5) = effective speed of  boat2 going upstream
:
Write a time equation; time = dist/speed (their travel times differ by 1 hr)
{{{44/((s-5))}}} - {{{75/((s+5))}}} = 1 hr
multiply by (s-5)(s+5), cancel the denominators
44(s+5) - 75(s-5) = (s+5)(s-5)
44s + 220 - 75s + 375 = s^2 - 25
-31s + 595 = s^2 - 25
Arrange as a quadratic equation
0 = s^2 + 31s - 25 - 595
s^2 + 31s - 620 = 0
Using the quadratic formula, I got a positive solution of 
s = 13.83 km/hr in still water
:
:
Check this find the actual time of boat1
75/18.83 ~ 4 hrs
find the time boat2
44/8.83 ~ 5 hrs, one hour difference