Represent Probability on a Cartesian Plane

[Delta11]

I have a problem
"
A train and a bus arrive at the station at random between 9 A.M. and 10 A.M. The train stops for 10 minutes and the bus for minutes. Find so that the probability that the bus and train meet equals 0.5"

One solution I found was using curves of train and bus departure times on a Cartesian plane. I get that, what i don't get is how to represent the given probability and calculate the area under the curve for this question.

You can find the solution for review here:
http://www.sciencechatforum.com/viewtopic.php?f=19&t=6604

 

[zorro]

In this figure,
x is the train time of arrival
y is the bus time of arrival
b is the stop time of the train (10 minutes)
a is t, stop time of the bus (the unknown)
T is 60 minutes



Assuming jointly uniform distribution of the two times of arrival, the event "meeting" is represented by the shaded area.
You must find "a" in such a way that the non shaded area is 0.5 times the area of the square.
That's the solution.

Regards

Z