Jack and Jill Waiting Time question.

Jack and Jill agree to meet at 1:30. If Jack arrives at a time uniformly distributed between 1:15 and 1:45, and if Jill **independently **arrives at a time uniformly distributed between 1:30 and 2,

1) What is the probability that Jack arrives first?

Straight forward enough. I figure it's 3/4.

2)What is the probability that Jack waits more that 15 minutes.

I think I'm stumped by this, maybe not. I set X to be the time after 1:15 that Jack arrives, and Y to be the time after 1:15 that Jill arrives. Am I correct in assuming that this is the way to solve it:

$\displaystyle \int_{15}^{45}\int_{0}^{y-15}f_{XY}(x,y)dxdy$