Final answer:
After calculating the total processing time by considering that arrivals take 3 times longer to process than departures, Tuesday will be the busiest at the front desk with a total time of 525x.
Step-by-step explanation:
To determine which day will be the busiest at the front desk, we need to consider the amount of time spent on processing arrivals and departures. Given that arrivals take 3 times as much time to process as departures, we can calculate the relative 'busyness' for each day.
For Tuesday, we have 150 arrivals and 75 departures. If one departure takes x amount of time, an arrival takes 3x, making the total time for Tuesday (150 arrivals * 3x) + (75 departures * x) = 450x + 75x = 525x.
For Wednesday, we have 100 arrivals and 100 departures. Thus, the total time for Wednesday is (100 arrivals * 3x) + (100 departures * x) = 300x + 100x = 400x.
For Thursday, we have 50 arrivals and 180 departures. The total time for Thursday is (50 arrivals * 3x) + (180 departures * x) = 150x + 180x = 330x.
Comparing these totals, Tuesday has the highest total time (525x), indicating it will be the busiest day at the front desk.