A plane flies from Springville to Brockton and then back to Springville. When there is no wind, the round trip takes 6 hours and 24 minutes, but when there is a wind blowing from Springville to Brockton at 50 miles per hour, the trip takes 6 hours and 40 minutes. How many miles is the distance from Springville to Brockton?
+36915 rate * time = distance
distance to and from is the same
r * 6.4 = 2d or r * 3.2 = d
d/(r-50) + d /(r+50) = 6.667 (I changed the minutes to hours)
3.2r /(r-50) + 3.2r (r+50) = 6.667
3.2r (r+50) + 3.2r ( r-50) = 6.667 ( r+50)(r-50)
3.2 r^2 + 160r + 3.2r^2 - 160r = 6.667 r^2 -16667.5
-.2667 r^2 + 16667.5 = 0 quadratic formula shows x = 250 m/hr
250 m/hr x 6.4 hrs = roundtrip distance = 1600 miles 800 miles one way
