Two people agreed to meet between 6:00 and 7:00 PM, and whoever came first would wait for 15 minutes. What is the probability that the two can meet?

As the title mentioned, there are two people, A and B, who agree to meet between 6:00 and 7:00 PM. Each person arrives at a random time within this interval, and the first to arrive will wait for 15 minutes before leaving. What is the probability that they will meet?

We can solve this problem using geometric probability. Let’s represent the arrival times of A and B on a coordinate plane where the x-axis represents the arrival time of A and the y-axis represents the arrival time of B. Both x and y range from 0 to 60 minutes (since 6:00 PM to 7:00 PM is a 60-minute interval).

The total possible outcomes can be represented by a 60x60 square on the coordinate plane.

For A and B to meet, the difference between their arrival times must be 15 minutes or less. This translates to the following conditions:

This can be broken down into two inequalities:

These inequalities represent two lines on the coordinate plane:

Visualizing:

The ratio of the area between these two lines to the area of ​​the square is our probability.