Create a departure timetable for two vehicles, a bus and a mini-bus, between 8:00 AM and 5:00 PM. Buses depart every 40 minutes, and mini-buses depart every 50 minutes. Both start at 8:00 AM.

Here is the solution to your problem:

Part 1: Draw a departure time table for 2 vehicles from 8:00 AM to 5:00 PM.

• Bus Departure Times (every 40 minutes): Starting at 8:00 AM, buses depart at: 8:00 AM, 8:40 AM, 9:20 AM, 10:00 AM, 10:40 AM, 11:20 AM, 12:00 PM, 12:40 PM, 1:20 PM, 2:00 PM, 2:40 PM, 3:20 PM, 4:00 PM, 4:40 PM.

• Mini-Bus Departure Times (every 50 minutes): Starting at 8:00 AM, mini-buses depart at: 8:00 AM, 8:50 AM, 9:40 AM, 10:30 AM, 11:20 AM, 12:10 PM, 1:00 PM, 1:50 PM, 2:40 PM, 3:30 PM, 4:20 PM.

Here is the departure time table:

Bus Departure Times	Mini-Bus Departure Times
8:00 AM	8:00 AM
8:40 AM	8:50 AM
9:20 AM	9:40 AM
10:00 AM	10:30 AM
10:40 AM	11:20 AM
11:20 AM	12:10 PM
12:00 PM	1:00 PM
12:40 PM	1:50 PM
1:20 PM	2:40 PM
2:00 PM	3:30 PM
2:40 PM	4:20 PM
3:20 PM
4:00 PM
4:40 PM

Part 2: Identify any time of the day when the two vehicles will leave the park at the same time.

To find when both vehicles leave at the same time, we need to find the Least Common Multiple (LCM) of their departure intervals, 40 minutes and 50 minutes.

Step 1: Find the prime factorization of 40 and 50.

$$40 = 2 \times 2 \times 2 \times 5 = 2^3 \times 5^1$$ $$50 = 2 \times 5 \times 5 = 2^1 \times 5^2$$

Step 2: Calculate the LCM.

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