+130555 Look at the following graph, Mellie........https://www.desmos.com/calculator/9p3hhbrwl2
The graph of all the possible arrival times - in minutes after 5 PM - by both Alice and Bob is bounded by x = 0, y = 0 x= 60 and y = 60.
Let the x values in the graph be the number of minutes after 5 PM that Alice arrives at the party. And let the y values be the number of minutes after 5 PM that Bob arrives at the party. For example, at (0,0), both arrive at 5PM and at (60,60), both arrive at 6 PM. At (0, 45)....Alice arrives at 5PM and Bob arrives at 5:45 PM. At (22.5, 22.5), both arrive at 5:22:30. And at (45, 0), Alice arrives 45 minutes after 5 PM and Bob arrives exactly at 5 PM.
But, the times we are interested in lie beneath the graph of x + y ≤ 45.
And this area is bounded by x = 0, y = 0 and x + y ≤ 45 . And it equals 45^2 / 2 = 1012.5 sq units
Note that the area of the total possible arrival times = 60 x 60 = 3600 sq units
So....the probabilty that the sum of Alice's and Bob's arrival times after 5PM are less than 45 minutes =
1012.5 / 3600 = 9/32
