Question

There are busses leaving all day long at 5 minutes past the hour, 25 minutes past the hour, and 40 minutes past the hour (=20 minutes to the hour), what is the average wait time, if half of all people arrive randomly over the hour (all day long, having no idea what the schedule is) and the other half of all people arrive [randomly] during the last 5 minutes before a bus departure? In total, 240 people arrive per hour. Solve the problem graphically or numerically.

Answer 1

Given,

1. Timing of bus 1 = 5 minutes past the hour

2. Timing of bus 2 = 25 minutes past the hour

3. Timing of bus 3 = 40 minutes past the hour

4. Frequency of passengers = 4 people per minutes i.e. 240 per hour

There will be three time spaces in which passengers have to wait.

Time space for bus 1 = 25 -5 = 20 minutes

Time space for bus 2 = 40 -25 = 15 minutes

Time space for bus 3 = 5 -40+60 = 25 minutes

First we will calculate average wait time for all passengers in each bus.

Total wait time for all passengers = 800 + 450 + 1250 = 2500 minutes

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