Uniform distribution Probability

[SMA_01]

John is going to eat at at McDonald's. The time of his arrival is uniformly distributed between 6PM and 7PM and it takes him 15 minutes to eat. Mary is also going to eat at McDonald's. The time of her arrival is uniformly distributed between 6:30PM and 7:15PM and it takes her 25 minutes to eat. Suppose the times of their two arrivals are independent of each other. What is the probability that there will be some time that they are both at McDonald's, i.e. their times at McDonald's overlap.

So let T= John's arrival time
and
S=Mary's arrival time


I don't really know where to go from here. Can anyone provide hints in the correct direction?

Thanks

 

[jbunniii]

Maybe try to find the probability that the times do not overlap. This can happen one of two ways: either John leaves before Mary arrives, or John arrives after Mary leaves. What are the probabilities of these two events?

 

[SMA_01]

Maybe try to find the probability that the times do not overlap. This can happen one of two ways: either John leaves before Mary arrives, or John arrives after Mary leaves. What are the probabilities of these two events?

Thank you. I'm a bit confused on how to find the density function, though.
For John, I'm guessing f(t)=1/60 for 0<t<60 and 0 otherwise
For Mary, g(s)=1/45 for 30<s<75 ?
Or is that completely off?

 

[HallsofIvy]

If t represents the number of minutes after 6:00, then, yes, those are correct.

 

[haruspex]

If t represents the number of minutes after 6:00, then, yes, those are correct.

... and if those functions are the density functions of the arrival times, as opposed to representing the probabilities of being present at time t.