<PRE><B>Question 466414</B>
During the first part of a trip, a canoeist travels 59 miles at a certain speed.
 The canoeist travels 25 miles on the second part of the trio at a speed of 5 mph slower.
 The total time for the trip is 5 hrs. What was the speed of each part of the trip.
:
Let s = speed on the 1st part of the trip
then
(s-5) = speed on the 2nd part
:
Write a time equation; time = dist/speed
:
1st part time + 2nd part time = 5 hrs
{{{59/s}}} + {{{25/((s-5))}}} = 5
multiply by s(s-5), results;
59(s-5) + 25s = 5s(s-5)
:
59s - 295 + 25s = 5s^2 - 25s
:
84s - 295 = 5s^2 - 25s
:
Arrange as a quadratic equation on the right
0 = 5s^2 - 25s - 84s + 295
:
5s^2 - 109s + 295 = 0
:
use the quadratic formula to find s, only one solution will make sense</PRE>