Wind affects the speed

If $v$ is the no-wind speed of the bike, and $w$ is the wind speed, and $d$ is the distance from home to school, then we have the following two equations:

$40 = \dfrac{d}{v - w}$

$30 = \dfrac{d}{v+w}$

Dividing the first equation by the second,

$\dfrac{4}{3} = \dfrac{v + w }{v-w} = \dfrac{ 1 + \frac{w}{v}}{1 - \frac{w}{v}}$

Solving for $\frac{w}{v}$ , we get $\frac{w}{v} = \frac{1}{7}$ .

Now from the first equation, $40 = \dfrac{d}{v - w} = \dfrac{ \frac{d}{v} }{1 - \frac{w}{v} }$

Therefore, $T = \dfrac{d}{v} = 40 ( 1 - \frac{w}{v} ) = 40 (1 - \frac{1}{7} ) = 40 (\frac{6}{7} ) = 34.285$ minutes.