Please explain the math of this situation to me. (funny video inside)

Factual Questions
1

Note: This is from Would I Lie To You?, a game where the celebrities read a card and the other team guesses if the statement is true or a lie.

I would, for the sake of entertainment, encourage you to watch the entire video of Lee Mack lying/telling-the-truth about abandoning someone who got stuck in a tree.

However, the part my brain is having a hard time understanding is the opening 45 seconds to a minute. Everything after the opening minute is irrelevant to this question.

Lee, the card reader, says that the man was “2/3 the way up the tree.” When asked how tall the tree was, he responds, “As high as the man was up, plus 1/3.”

David(on the other team) points out that the man must have been 3/4 the way up the tree, then. He says, “If he was 2/3 the way up the tree, then the height of the tree was how high he was up, plus a half.”

Hey, I guess I’m ignorant because I can not process the information in the exchange they have. I would have understood it as Lee said it. He was 2/3 the way up the tree, there for that height plus the remaining 1/3 is the height of the tree.

What the heck is David critiquing? Everyone kind of claps and acknowledges his point, but I can’t get it through my mind.

Can anyone here explain or illustrate?

2

1/3 is half of 2/3.
3/3 = 2/3 + (one half of 2/3).

1/4 is a third of 3/4.
4/4 = 3/4 + (one third of 3/4)

3

Put another way: say the tree is 30 feet tall, and the climber is 20 feet up; how tall is that tree? 20 plus one-third of 20, or 20 plus half of 20?

4

Of course, if you like, the height of the tree was 2/3 of the height of the tree plus 1/3 (of the height of the tree), as originally intended :slight_smile: All parties are just having a bit of fun.