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To find the minimum time of flight for a projectile striking an inclined plane, we can use the following steps:

1. **Understanding the Problem**: The projectile is launched with an initial velocity \( u \) at an angle \( \theta \) with respect to the horizontal, and it strikes an inclined plane at an angle \( \alpha \) with respect to the horizontal. The horizontal distance from the point of projection to the inclined plane is \( d \).

2. **Equations of Motion**: The horizontal and vertical motions can be expressed as:
\[ x = u \cos(\theta) t \]
\[ y = u \sin(\theta) t - \frac{1}{2} g t^2 \]
where \( g \) is the acceleration due to gravity.

3. **Finding the Equation of the Inclined Plane**: The equation of the inclined plane can be expressed as \( y = x \tan(\alpha) \).

4. **Eliminating Time**: We substitute the expression for \( x \) from the first equation into the equation of the inclined plane:
\[ y = \tan(\alpha) \, (u \cos(\theta) t) \]

5. **Setting Up the Equation**: Now using the second equation of motion, we have:
\[ u \sin(\theta) t - \frac{1}{2} g t^2 = \tan(\alpha) (u \cos(\theta) t) \]

6. **Finding Minimum Time**: Rearranging the equation gives a quadratic in terms of \( t \), which you can solve using the quadratic formula. The final relation for the minimum time can be simplified and solved for \( t \).

7. **Final Expression**: On solving the above relationship, the time can be represented as:
\[ t_{min} = \frac{d}{u \cos(\theta) \cos(\alpha)} \]

8. **Conclusion**: Therefore, to minimize the time taken by the projectile to reach the incline, the angle \( \theta \) can be adjusted and you can calculate \( t_{min} \) based on the initial velocity, angle of inclination, and distance \( d \). Thus, the answer is derived as per these considerations.