SOLUTION: Two skiers set out together on a long track, one skied a quarter of a mile per hour faster than the other and finished an hour earlier, if both skied 34 miles at what rate did each

Question 848438: Two skiers set out together on a long track, one skied a quarter of a mile per hour faster than the other and finished an hour earlier, if both skied 34 miles at what rate did each of them ski
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Two skiers set out together on a long track, one skied a quarter of a mile per hour faster than the other and finished an hour earlier,
if both skied 34 miles at what rate did each of them ski
:
let s = speed of the 1st skier
then
(s+.25) = speed of the faster skier
:
Write a time equation; time = dist/speed
1stskier time - fast skier time = 1 hr
- = 1
multiply by s(s+.25), to cancel the denominators, resulting in:
34s(s+.25) - 34s = s(s+.25)
34s + 8.5 - 34s = s^2 + .25s
A quadratic equation
s^2 + .25s - 8.5 = 0
use the quadratic formula to find s, I got a postive solution of
s = 2.793 mph, speed of the 1st skier
then
2.793 + .25 = 3.043 mph, speed of the faster skier
;
;
Confirm this by finding the actual time of each.
34/2.793 = 12.173 hrs
34/3.043 = 11.173
-----------------
time dif: 1 hr
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