A probability question:
Two friends agreed to meet in a coffee shop in the time interval of $9:00AM-10:00AM$. Each one is coming on a random time in this interval, and stays for 10 minutes.
What is the probability that they will meet?
My try:
Denote $X$ as first friend coming time and $Y$ as second friend coming time. $X, Y$ ~ $U(0,60)
I need to find $P(|X-Y| < 10) = P(X - Y < 10) + P(Y - X < 10)$
Start: $P(X - Y < 10) = (X < 10 + Y) $
Drawing a triangle gives a probability of $\frac{12.5}{200}$.
But it's not one of the possible answers. Can you help me please? Thanks in advance.