Question 398287: Anne and Robert decide to meet between 6 and 7 pm for dinner but agree that each should wait no longer than 10 minutes for the other. Find the probability that they meet.
Answer by robertb(5830)   (Show Source):
You can put this solution on YOUR website! Let x = # minutes after 6 pm when Anne came, and
y = # minutes after 6 pm when Robert came.
Then the sample space S = {(x,y):  ,  } is the (open) square with vertices (0,0), (0,60), (60,0), and (60,60).
What is wanted is the intersection of the sample space S with the region satisfying
 , or equivalently,
-10 < y-x < 10.
The boundaries of this double inequality are the lines y - x = -10 and y - x = 10.
All points between these two lines (excluding the lines themselves) satisfy the preceding double inequality. Call this region R.
Then what is desired is the area of S intersection R. This area is equal to  , where  = area of sample space S, and  = the area of S-R.
Then the probability is equal to  .
Incidentally, S-R consists of two congruent triangles  and  .
has vertices (0,10), (50,0), (50,60)
has vertices (10,0), (60,0), (60,50)
(Each triangle has area  .)
The probability that Anne and Robert meet is then
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