Joint uniform distribution two different intervals

Question

I have a problem with the following exercise:

X corresponds to the duration of Paul’s commute to work, and Y to the duration of Peter’s. X is uniformly distributed in [15, 25] and Y in [15, 30]. X and Y are assumed to be independent. What is the probability that Peter and Paul both take more than 20 minutes to get to work?

Everything I know is that I have to use the joint probability density function.

Answer 1

Hint:

"Everything I know is that I have to use the joint probability density function..."

The independence of $X$ and $Y$ tells you the opposite.

You are asked to find: $$P(X>20,Y>20)$$ where $\{X>20\}$ and $\{Y>20\}$ are independent events.