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?

(A) 12 minutes

(B) 18 minutes

(C) 48 minutes

(D) 1 hour, 12 minutes

(E) 1 hour, 20 minutes

least waiting time = 18 mins

Explanation:

given as per question we know that 2nd bus start 10 min early than 1st bus

and both time frequency same = 30 min

1st bus time take = 1 hr 12 mins

and 2nd bus get waiting time 30 min - (10 + 12)

that is = 8 mins

so

we can say time arrival time for 1st bus = 8:32 and 9:02 and 9:32

by adding 30 mins

and

departure time for 2nd bus = 8:40 and 9:10 and 9:40

same like that 3rd bus leave every hour

and

service start on hour clock, a 10 mins early is = 7:10 am and 9 am

frequency of either half or 1 hour

so 2nd bus takes = 2 hour 40 mins

so waiting time is 60 - (10 - 40) = 10 min or 10 + 30 = 40 mins

so 1st bus waiting time is 8 mins so it take least time 10 mins for 2nd bus waiting time

as that

least waiting time = 8 + 10

least waiting time = 18 mins