This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
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 × 2 × 2 × 5 = 2^3 × 5^1 50 = 2 × 5 × 5 = 2^1 × 5^2 Step 2: Calculate the LCM. LCM(40,