Lucas and Gordon both take their dogs (Ernie and Bella, respectively) to the dog park for 10 minutes each morning between 7:00am and 8:00am, at times independent of one another. But Lucas tends to arrive closer to 8:00am, while Gordon tends to arrive closer to 7:00am. To be precise, the number of minutes X after 7:00am at which Lucas arrives has probability density function given by fX(x) =

x/1800 ; if 0 < x < 60; 0; otherwise. and the number of minutes Y after 7:00am at which Gordon arrives has probability density function given by fY (y) =

1/30 -y/1800 ; if 0 < y < 60; 0; otherwise. (a) Find the probability that Gordon arrives before Lucas. (b) Find the probability that Lucas and Gordon see each other at the dog park.