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Scott Cram
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The night before she was to leave for her dream vacation around the world, Sally Forth, at home in Alphaville, couldn't find the passport she had picked up that afternoon in the city of Hope Springs. As she was desperately looking through her briefcase for the fourth time, the phone rang. Her passport was at the Hope Springs railroad station.

The following morning, a few minutes before 7:00, Sally arrives at the Alphaville train station. In order to catch her flight to Europe from the Alphaville airport, she has to make the round trip to Hope Springs and back before noon. The timetables for eastbound and westbound travel between Alphaville and Hope Springs are shown below. Each horizontal row in each of the two timetables represents a different train. Dashes appear at station where the train does not stop. A series of Xs indicates the end of the line. The periods, of course, are simply to keep the spacing correct. For example, the 7:00 train from Alphaville stops only at Fortuna, which is the end of its route; while the 7:10 from Alphaville stops at every station, arriving at Hope Springs at noon.

Sally can wait at stations, transfer from one train to another, and change directions as often as she wishes. For example, she might take an eastbound train part of the way to Hope Springs, then switch to a westbound train in order to catch a faster eastbound train at another station.

Assume that all trains are running on time, that transferring to another train takes less than four minutes, and that picking up the passport at Lost & Found takes only a minute. Can you find the one way that Sally can make it from Alphaville to Hope Springs and back before noon?



EASTBOUND (times of departure) All times are A.M. unless shown in boldface.

Alphaville..Betaville..Clarksville..Discovery..Ephemeral..Fortuna..Gamesport..Hope Springs
..7:00...........---............---.............---.............---.........8:10.........XXX............XXX
..7:10.........7:40.........8:30..........9:10........10:00.......10:30.......11:20........12:00
..XXX.........7:20.........7:50..........8:10............---.........8:40.........XXX............XXX
..7:20...........---............---...........7:50............---.........8:30.........9:00...........9:30
..XXX.........7:30..........8:20...........---.............---...........---...........8:50...........9:00
..7:40.........8:10...........---...........8:50............---.........9:20.........9:40..........10:00
..XXX.........7:50............---..........8:10............---.........8:40.........XXX............XXX
..7:50...........---............---.............---...........8:30........9:00.........9:20...........9:40
..8:30.........9:00...........---.............---...........9:30........9:50.......10:20..........10:50
..XXX..........XXX.........8:40............---............---............---..........9:10...........XXX
..9:30.......10:00...........---..........10:30...........---........11:00..........---............11:30
.10:10......10:50.........11:30...........---.........12:00.........XXX........XXX...........XXX



WESTBOUND (times of departure) All times are A.M. unless shown in boldface.

Hope Springs..Gamesport..Fortuna..Ephemeral..Discovery..Clarksville..Betaville..Alphaville
..7:00...................---.........7:20.........7:40.........8:00..........8:10.........---.........9:00
..7:10.................7:30........8:00.........8:20.........9:00..........9:30.......10:10.....10:50
..7:50.................8:20........8:50.........9:10..........---............9:40.........---........10:20
..8:20.................8:40.........---............---............---...........10:00........XXX.......XXX
..8:50...................---..........---............---...........9:40...........---...........---........11:10
..9:10...................---..........---............---...........9:50..........XXX.........XXX.......XXX
..9:15...................---..........---............---..........10:05.........XXX.........XXX.......XXX
..9:20...................---..........---...........9:40........10:00..........---.........10:30......XXX
..9:50................10:10........---..........10:30........10:50..........---.........11:20......XXX
..XXX..................XXX........XXX........10:10..........---.............---.........10:40......XXX
.10:20..................---........10:50.........---...........11:10..........---.........11:30.....12:05
..XXX..................XXX.......10:40.........---.............---...........11:20........---........11:50
pxs
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284 Posts

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7.20 Eastbound from Alphaville
Gets off at Discovery at 7.50

8.00 Westbound from Discovery
Gets off at Clarksville at 8.10

8.20 Eastbound from Clarksville
Gets off at Hope Springs at 9.00

Picks up Passport

9.20 Westbound from Hope Springs
Gets off at Ephemeral at 9.40

10.00 Eastbound from Ephemeral
Gets off at Fortuna at 10.30

10.40 Westbound from Fortuna
Gets off at Alphaville at 11.50

Phew!
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