In the wilderness
The other day I went for a three and a half hour hike in the wilderness with my boss alone. In any continuous one-hour period during our hike we covered exactly 2 km.
How many people went on the hike? How long was it?
Problem source: MathCamp 2009 via mathpuzzle.
December 1st, 2009 at 3:42 am
>How many people went on the hike?
This is a verbal quibble. “Went…with my boss alone” could mean that you went only with your boss, i.e. 2 people went, namely you and your boss. Or it could mean that you went alone, and also that you went with your boss, which is yourself, as you are self-employed.
>How long was it?
Not enough info. Let x be the distance covered in the first half-hour, and y = 2 km - x. Then in the 7 half-hours of the trek, you covered x, y, x, y, x, y and x. Not enough info is provided to determine x and y separately.
December 1st, 2009 at 6:18 am
At its most simplistic, you hiked at a rate of 2 km / hr over 3.5 hours so you hiked 7 km total. It can’t possibly be that easy, so I’m looking forward to the follow-up questions that sometimes come.
December 1st, 2009 at 6:21 am
If there is not enough information to calculate the length of the hike, what about the minimum and maximum possible distances?
December 1st, 2009 at 11:02 am
Perhaps “how long” does not refer to distance but time. Therefore, the hike was three and a half hours long.
December 1st, 2009 at 8:32 pm
If, in Richard’s expression, x = 2 km, they went 8 km. If y = 2 km, the total distance is 6 km. That provides the range of possible distances, though if they went 6 km, it was actually a 2.5 hour hike.