<PRE><B>Question 963557</B>
Kelly rollerblades for 12 miles, then slows down by 4 miles per hour for another 6 miles.
 The slower portion takes 15 minutes less than the first part.
 Find the total time she spent rollerblading, if you know it was not more than 1 hour and 30 minutes.
:
let s = speed on the first 12 mi
then
(s-4) = speed on te last 6 mi
:
Change 15 min to 1/4hr
:
Write a time equation; time = dist/speed
:
fast speed time = slower speed time +  1/4 hr
{{{12/s}}} = {{{6/((s-4))}}} + {{{1/4}}}
multiply equation by 4s(s-4), cancel the denominators and we have:
12*4(s-4) = 6(4s) + s(s-4)
12(4s-16) = 24s + s^2 - 4s
48s - 192 =  s^2 + 20s
Combine on the right to form a quadratic equation
0 = s^2 + 20s - 48s + 192 
s^2 - 28s + 192 = 0
This will factor to
(s-12)(s-16) = 0
Two solutions
s = 12 mph
or 
s = 16 mph
:
Lets use the faster speed s=16 mph for the first 12 mi, and 12 mph for the last 6
Find the times
12/16 = .75 hrs
6/12  = .50 hr
---------------
tot time: 1.25 hrs, 1 hr 15 min
less than 1 hr 30 min</PRE>