<PRE><B>Question 305501</B>
The members of a bicycle club rode a 20-mile round trip route. On the way back, they had a tailwind and averaged 3 mph faster than on the first 10 miles of the trip. If the entire trip took them 1 1/2 hours, what was their average speed on the first half of the ride?
-------------------------------
d = distance one way = 10 miles
r = rate going without tailwind
d/r + d/(r+3) = 1.5
10/r + 10/(r+3) = 1.5
10(r+3) + 10r = 1.5r(r+3)
{{{20r + 30 = 1.5r^2 + 4.5r}}}
{{{3r^3 - 31r - 60 = 0}}}
*[invoke solve_quadratic_equation 3,-31,-60]
---------------
Ignore the negative solution
r = 12 mph (1st half)
</PRE>