# Airport Shuttle

A shuttle transfers passengers from 5:30 to 22:30, on a route between an airport and 3 hotels. The shuttle departs the airport every hour on the hour and drops off passengers at the hotels always in the same order (airport->Sheraton->Hilton->Carlson) and with fixed travel times between station pairs:

Airport - Sheraton : 21 min
Sheraton - Hilton  : 5 min
Hilton - Carlson   : 4 min
Carlson - Airport  : 30 min


On Wednesday Eddie got on a shuttle from his hotel to the airport exactly 2 hours before his flight. To Eddie’s surprise, the ride to the airport took 8 minutes less than it took on the previous Thursday when he stayed at that same hotel and had to catch a 13:30 flight.

What time was Eddie’s flight on Wednesday?

Hint 1:

Note that the "same order" of stations refers only to dropping off passengers at the hotels.

• How is that possible? You said the ride takes exactly the same time to get from his hotel to the airport each time. May 28 '16 at 13:04
• What is a round hour? Does it mean on the hour? May 28 '16 at 13:22
• @LeppyR64 yes, on X:00 May 28 '16 at 13:28
• @JoeZ. it accidentally said 5 minutes less. the correct number is 8 minutes less, fixed it now. May 28 '16 at 20:25
• @2012rcampion zero time, for the purpose of this puzzle. May 28 '16 at 20:49

The bus actually travels both ways on the path between the airport and the hotels — the route is 30 minutes there and 30 minutes back for a reason. However, when it leaves Carlson, it never drops anyone off until it reaches the airport.

The normal schedule looks like this:

Airport    :00  (dropoff and pickup)
Sheraton   :21  (dropoff and pickup)
Hilton     :26  (dropoff and pickup)
Carlson    :30  (dropoff and pickup)
Airport   1:00


But since the shuttle bus starts at 05:30 every morning, it actually starts off at the Carlson hotel. On the first trip of the day only (from 05:30 to 06:00), it picks people up from all three hotels on the way to the airport, dropping them all off once it arrives, as a service to the early riders from the other two hotels who shouldn't have to wait a whole hour more for the shuttle bus.

Carlson    :30  (pickup only)
Hilton     :34  (pickup only)
Sheraton   :39  (pickup only)
Airport   1:00  (dropoff and pickup)


So if Eddie lives at the Hilton, he will board the bus at 05:34 and arrive at 06:00, for a trip time of 26 minutes. Since he boarded the bus at 05:34, his plane is scheduled to leave at 07:34.

But for subsequent trips, it will go from Carlson straight to the airport without any more pickup stops because it has already visited the hotels a short time earlier, and visits each location every hour on the specified minutes. So if Eddie was catching a 13:30 flight, he'd have to board the bus at 11:26 to arrive at 12:00, for a trip time of 34 minutes, which is 8 minutes more than if he had boarded the first bus of the day as above.

• And the last trip of the day would be from 22:00 to 22:30, dropping people off at the hotels only, and not picking anybody up.
– user88
May 28 '16 at 22:06
• interesting actually very good haha I like it May 29 '16 at 9:28