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

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