Expectation of waiting time

[Guest]

A boy and a girl arrive separately to a place randomly within 60 minutes. They are willing to wait for one another
for 20 mins.
(1) What is the probability of their meeting at the place?
(2)What is the expectation of the waiting time for any one of them?


mr.wong

[Guest]

If a graph ( 2-dimensional ) can be drawn , answer of (1) will be shown to be 5/9 .
Based on this graph , plot a 3-dimensional graph with z-axis denoting
the waiting time of one of them , say the boy . Then calculate the volume
of the corresponding polyhedra , divided by the area of the base , perhaps
the answer of (2) may be found .


mr.wong

[Guest]

The answer of (2) has been found to be 310 / 27 mins . ( about 11.5 mins )


mr.wong

[Guest]

Sorry ! The above answer is incorrect .
The correct answer for (2) should be 260 / 27 mins.


mr.wong