Cumulative distribution function for min(X, 15)
Solution 1:
If Alice's waiting time is less than 15 minutes the CDF is the same as $F_X(x)$ but if the waiting time is 15 minutes or more she leaves. Thus the resulting CDF is
$$F_Y(y)=[1-e^{-y/10}]\cdot\mathbb{1}_{(0;15)}(y)+\mathbb{1}_{[15;\infty)}(y)$$
as you can see, there is a "jump" in $y=15$ thus the rv is not absolutely continuous.