Annie and Xenas each arrive at a party at a random time between 2:00 and 4:00.  Each stays for 45 minutes and then leaves.  What is the probability that Annie and Xenas see each other at the party?
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Annie and Xenas each arrive at a party at a random time between 2:00 and 4:00.  Each stays for 45 minutes and then leaves.  What is the probability that Annie and Xenas see each other at the party?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\dfrac{39}{64}
Annie and Xenas each arrive at a party at a random time between 2:00 and 4:00.  Each stays for 45 minutes and then leaves.  What is the probability that Annie and Xenas see each other at the party?
train