A person rides a bike against the wind at 8 mph when he goes back the wind helps him. He traveled 4 miles total 2 to the shop and 2 back. If the round trip was 30 minutes longwhat is thomas's speed on the bike without the wind.
+128475 Distance / Rate = Time
30 mi = 1/2 hr
2 / ( r - 8) + 2 / ( r + 8) = 1/2 where r is his rate in still air
Multiply through by 2
4 / (r - 8) + 4/(r + 8) = 1
[4 ( r + 8) + 4(r - 8)] / [ (r -8) (r + 8) = 1
8r = (r - 8) (r + 8)
8r = r^2 - 64
r^2 - 8r - 64 = 0
r^2 - 8r = 64
r^2 -8r + 16 = 64 + 16
(r - 4)^2 = 80 take the positive root
r -4 = sqrt (80)
r = sqrt (80) + 4 ≈ 12.9 mph = his rate in still air
