A drive$-$thru has one window for payment and one window for food delivery. Assume one vehicle leaves the payment window and arrives at the delivery window. A second vehicle in line behind the first vehicle arrives to the payment window at the same time. You want to simulate the time it takes for each vehicle to be processed at its respective window.

The processing time for the payment window follows a triangular distribution with a minimum of $20$ seconds, a most likely of $50$ seconds, and a maximum of $120$ seconds. The processing time for the delivery window follows a triangular distribution with a minimum of $55$ seconds, a most likely of $140$ seconds, and a maximum of $240$ seconds $($i$.$e$.,4$ minutes$)$

The computer generates a uniform random number $0\mathrm{.}796$ for the second vehicle $($at the payment window$)$ and a uniform random number $0\mathrm{.}228$ for the first vehicle $($at the delivery window$).$

Based on these uniform random numbers, which process finishes first and how long $($in seconds$)$ does it take that process to finish?