Shawn is planning a bus trip across town that involves three buses. Bus 1 travels between Shawn’s house and downtown, and it leaves every half-hour starting at 7:20 AM. Shawn will need to be on bus 1 for 1.2 hours. Bus 2 travels between downtown and uptown every half-hour starting at 7:10 AM. Shawn will need to be on bus 2 for 2/3 hour. Lastly, bus 3 travels between uptown and Shawn’s destination every hour starting at 9 AM. Assuming all buses stay on schedule, what is the least amount of time Shawn must spend waiting for buses? Choose the correct choice from the following choices: A) 12 minutes B) 18 minutes C) 48 minutes D) 1 hour, 12 minutes E) 1 hour, 20 minutes
Here's my solution. My first approach was to brute force the objective function in this optimization problem, minimize time spent waiting between buses   Givens:   1.2 hour=1 hour,12 minutes   2 2/3 hour=2 hour,40 minutes   Once you start filling out a table, you realize that there's only 2 solutions to this problem, leaving at the 20 minute mark of any hour versus leaving at the 50 minute mark of any hour.   [Reveal]Spoiler:   Answer, 18 minutes
<result>B</result>
Shawn is planning a bus trip across town that involves three buses. Bus 1 travels between Shawn’s house and downtown, and it leaves every half-hour starting at 7:20 AM. Shawn will need to be on bus 1 for 1.2 hours. Bus 2 travels between downtown and uptown every half-hour starting at 7:10 AM. Shawn will need to be on bus 2 for 2/3 hour. Lastly, bus 3 travels between uptown and Shawn’s destination every hour starting at 9 AM. Assuming all buses stay on schedule, what is the least amount of time Shawn must spend waiting for buses?