Brain Teaser - Riding against the wind

[Gerson W. Barbosa]

#1 only:

r = rider's speed
w = wind speed

r + w = 1/3 mi/min (1)
r - w = 1/4 mi/min (2)

From (1), w = 1/3 - r

Replacing this in (2) it follows that

r - 1/4 = 1/3 - r
2*r = 1/3 + 1/4
2*r = 7/12

r = 7/24 [mi/min]

t = 1 [mi]/(7/24 [mi/min]

t = 24/7 [min]