find the probability both planes can park at a gate 
Two airplanes are supposed to park at the same gate of a concourse. The arrival times of the airplanes are independent and randomly distributed throughout the 24 hours of the day. What is the probability both can park at the gate, provided the first to arrive will stay for two hours, while the second can wait behind it for one hour?

The question seems a little ambiguous to me, and I think an example would help. Suppose the first plane arrives at hour 0. Then it'll stay for 2 hours, so as long as the second arrives within that time, can't both airplanes park? What's the significance of saying "The second can wait behind the first one for one hour"?
I found the solution below, but I have some questions about it:

*

*Can someone elaborate on why the desired region is obtained by removing the points satisfying $x-1 \leq y \leq x+1$ and $x-2\leq y\leq x+2$?


 A: The intended interpretation seems to be that if one airplane is still parked at the gate when the other airplane arrives, the second airplane cannot park at the gate until the first airplane leaves.
I would have thought that the significance of "the second can wait behind it for one hour" is that if the second aircraft arrives when the first aircraft is parked at the gate, but the first aircraft is expected to leave within one hour, the second aircraft will wait and park at the gate after the first aircraft leaves.
But if the first aircraft is already parked and will be there for more than an hour after the second aircraft arrives, the second aircraft will park at another gate.
So the aircraft will both park at the same gate as long as their arrival times are more than one hour apart.
If they arrive less than one hour apart then the first arriving aircraft will be at the gate for more than an hour after the second aircraft arrives.
The solution might be a little clearer if you looked at Figure $110$.
(It's hard to say for sure since I have not seen that figure myself.)
However, the formulas $\lvert x - y - 1\rvert \leq 1$
and $\lvert x - y + 1\rvert \leq 1$ appear to be errors.
I think the correct formulas are $\lvert x - y - 24\rvert \leq 1$
and $\lvert x - y + 24\rvert \leq 1$.
These conditions appear to be based on an assumption that the two aircraft do not just arrive randomly within the $24$ hours of one day,
but that they each arrive every day, sometime within that day's $24$ hours.
So we could have a case where one aircraft arrives at the gate at
$11{:}45$ pm one day ($x = 23.75$) and the other aircraft arrives at $12{:}15$ am the next day ($y = 0.25$).  Here $x-y = 23.5$ so the condition
$\lvert x - y\rvert \leq 1$ is false, and you might think the two aircraft can both park, but actually the second aircraft arrives only half an hour after the first one and it will not be able to use the same gate.
