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 A Boy, a Girl, a Dog, and a Bicycle (Posted on 2004-02-03)
A boy, a girl and a dog go for a 10 mile walk. The boy and girl can walk at 2 mph and the dog can trot at 4 mph.

They also have a bicycle which only one of them (including the dog!) can use at a time.
When riding, the boy and girl can travel at 12 mph while the dog can pedal at 16 mph.

What is the shortest time in which all three can complete the trip?

 Submitted by DJ Rating: 4.4000 (10 votes) Solution: (Hide) 2 hours, 45 minutes First note that there's no apparent way to benefit from letting either the boy or girl ride the bike longer than the other. Any solution which gets the boy there faster, must involve him using the bike (forward) more; similarly for the girl. Thus the bike must go backwards more for it to remain within the 10-mile route. Thus the dog won't make it there in time. So the solution assumes they ride the bike for the same amount of time. Also note that there's no apparent way to benefit from letting any of the three arrive at the finish ahead of the others. If they do, they can probably take time out to help the others. So the solution assumes they all finish at the same time. The boy starts off on the bike, and travels 5.4 miles. At this point, he drops the bike and completes the rest of the trip on foot. The dog eventually reaches the bike, and takes it backward .8 miles (so the girl gets to it sooner) and then returns to trotting. Finally, the girl makes it to the bike and rides it to the end. The answer is 2.75 hours.

 Subject Author Date Puzzle Solution K Sengupta 2008-06-06 01:46:51 answer K Sengupta 2007-07-28 12:48:00 re: A Boy, a Girl, a Dog, and a Bicycle Richard 2004-02-11 21:11:39 A Boy, a Girl, a Dog, and a Bicycle Chuck Horn 2004-02-11 14:25:17 re(4): solution dave domingo 2004-02-04 15:15:36 re(3): solution Brian Wainscott 2004-02-04 13:38:30 re(3): solution SilverKnight 2004-02-04 13:02:53 re(2): solution dave domingo 2004-02-04 12:48:31 Solution Brian Smith 2004-02-04 10:44:36 re(2): Better late than never... SilverKnight 2004-02-04 06:23:12 re: Better late than never... Jils 2004-02-04 06:17:46 Another meanie on the flooble website ?? Penny 2004-02-04 00:00:59 my answer meanie 2004-02-03 22:04:36 re: Better late than never... Richard 2004-02-03 20:40:21 Better late than never... Brian Wainscott 2004-02-03 19:24:17 re: solution SilverKnight 2004-02-03 14:58:07 solution dave domingo 2004-02-03 14:37:22 i know how but not how fast dave domingo 2004-02-03 14:19:34 Solution steve 2004-02-03 13:59:17 Theoretical minimum that can't be done logistically. Charlie 2004-02-03 13:40:35 fun dave domingo 2004-02-03 13:33:03

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