<PRE><B>Question 888685</B>
 Felipe jogs for 12 miles and then walks another 12 miles.
 He jogs 2.5 miles per hour faster than he walks, and the entire distance of 24 miles takes 11 hours.
 Find the rate at which he walks and the rate at which he jogs.
:
Let s = his walking speed
then
(s+2.5) = his jogging speed
:
Write a time equation, time = dist/speed
{{{12/((s+2.5))}}} + {{{12/s}}} = 11
multiply by s(s+2.5), cancel the denominators and you have:
12s + 12(s+2.5) = 11s(s+2.5)
12s + 12s + 30 = 11s^2 + 27.5s
Combine on the right to form a quadratic equation
0 = 11s^2 + 27.5s - 24s - 30 
11s^2 + 3.5s - 30 = 0
Use the quadratic formula to find s, I got a positive solution of:
s = 1.5 mph is his walking speed
and 2.5 mph faster:
4 mph is his jogging speed
;
:
Check this by finding the actual time of each.
12/1.5 =8 hrs
12/4  = 3 hrs
-------------
Total time 11 hrs</PRE>