SOLUTION: 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 spen

Question 963557: 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.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
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
= +
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
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