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Might Merely Meet (Posted on 2005-06-07) Difficulty: 2 of 5
A boy and a girl agree to meet in the park. Each will show up at a random time between 12:00 and 13:00, and wait for the other person 20 minutes, but not past 13:00.

What is the probability that they will actually meet?

See The Solution Submitted by Old Original Oskar!    
Rating: 4.0000 (5 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: Solution + Spoiler (Ups...) | Comment 2 of 12 |
(In reply to Solution + Spoiler by ajosin)

Did I say 280/360 = 7/9?, I meant to say 200/360 = 5/9.

I made a mistake while doing the area of the trapezoide,

20+21+22+....+39+40+....40+39 + ....+22+21+20 =200

There are 60 terms in the sum, 20 of which are 40's.

There is another way to solve this by drawing a 60X60 area and shading out the times where they do not meet (from the diagonal, the regions that are more than 20 min away in the x or y directions). Youll get two triangles with a total area of 160 min^2. Therefore the porbability of them meeting is p = 1- 160/360 = 1- 4/9 = 5/9.

Edited on June 7, 2005, 7:03 pm
  Posted by ajosin on 2005-06-07 19:00:50

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