All the villagers in the realm of King Arthur were invited to a Christmas gala held at the king’s castle. Alf and his wife Beryl, left their cottage at 11 AM that morning and traveled by ox cart to the castle. At 11:30 AM, an eager and impatient Beryl asked Alf, who was driving at a fast pace, “How far have we gone, dear?”

Alf replied, “Three times as far as the distance from here to the inn, where I will stop and have some nourishment.”

The couple stopped at the inn for food and departed at 1:00 PM to continue their journey. Having overeaten, Alf became sleepy and drove much slower than before their stop at the inn. Afraid of being late, Beryl asked her husband, at 2:00 PM, exactly 2 miles from the point where she had asked her first question, “Do we have much further to go Alf?”

Alf mumbled, “Three times as far as we have come since leaving the inn.”

Beryl then demanded that she take over the driving, to which a sleepy Alf readily agreed. The couple finally arrived at the castle at 3:30 in the afternoon. Despite the long journey, both thoroughly enjoyed all the festivities.

What was the distance from the couple’s cottage to the castle?

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That’s not the answer the RiddleDude came up with. Can you show your work? Oh, and we’re just looking for the miles here, not the time.

8 miles.

You’re correct, Geoff.

Here is how the RiddleDude came up with his answer:

What was the distance from the couple’s cottage to the castle?

Their cottage shall be A

The inn shall be B

The castle shall be C

Mark a point D between A and B, this is where they were at 11:30 AM when she first asked her husband about the distances. From his response we can gather that they have gone 3/4 of the way from A to B

Mark a point E between B and C. From the husband’s response at this point we gather that they have gone 1/4 the distance from B to C.

Two letters next to each other mean the distance between them, i.e., AC = AB + BC

Therefore:

(1/4)AB + (1/4)BC = 2 miles, because that was the difference between the two questions’ locations. Multiply everything by four (because it was only ¼ of the way).

AB + BC = 8 miles = AC

Geoff, you’re today’s winner!