A city's public transportation system wants to improve its bus network efficiency. They currently operate 200 buses on 20 different routes, with each route having a varying number of stops. If they can find a way to reduce the average waiting time at each stop by 2 minutes, calculate the potential time saved per day for all passengers, assuming an average of 50 passengers boarding at each stop and 12 hours of operation per day. Provide step-by-step reasoning.

Step 1: Calculate the total number of stops in the bus network.
Since there are 20 different routes and each route has a varying number of stops, we cannot find an exact number for this. However, we can use a variable to represent the total number of stops. Let's call it S.

Step 2: Calculate the potential time saved per stop.
If they can reduce the average waiting time at each stop by 2 minutes, then each passenger would save 2 minutes of waiting time per stop.

Step 3: Calculate the potential time saved per day for all passengers at one stop.
Assuming an average of 50 passengers boarding at each stop, the potential time saved per day for all passengers at one stop would be:
50 passengers * 2 minutes = 100 minutes

Step 4: Calculate the potential time saved per day for all passengers at all stops.
To find the potential time saved per day for all passengers at all stops, multiply the potential time saved per day for all passengers at one stop (100 minutes) by the total number of stops (S):
100 minutes/stop * S stops = 100S minutes

Step 5: Convert the potential time saved per day for all passengers from minutes to hours.
To convert the potential time saved per day for all passengers from minutes to hours, divide the result from Step 4 by 60:
100S minutes / 60 = (100/60)S hours

So, the potential time saved per day for all passengers is (100/60)S hours, where S represents the total number of stops in the bus network.