WMC 2018 Senior Problem 6
Jeri and Tina are two retired teachers who agree to meet for lunch. However, they both forgot the exact time they planned to meet. They both remember it is between 4 pm and 5 pm, but they do not recall the exact time. Independently, they decide to arrive at a random time between 4 and 5 and wait for 10 minutes. If the other teacher does not show up in 10 minutes, they will leave. What is the probability that the two teachers will meet?
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1 solution
Let x and y be the number of minutes after 4pm Jeri and Tina arrive, respectively. We can plot their arrival times on coordinate axes.
Clearly, they will meet if ∣ x − y ∣ ≤ 1 0 . Here it is, represented on a graph.
We can calculate the probability by getting the area of the red region and dividing it by the area of the square. This gives 3 6 0 0 3 6 0 0 − ( 5 0 ⋅ 5 0 ) = 3 6 0 0 1 1 0 0 = 3 6 1 1 .