# Answers to Knot I explained — A Tangled Tale

> Chapter companion for A Tangled Tale by Lewis Carroll.

## What happens

The chapter presents the solution to a puzzle about two travelers walking on level ground, up a hill, and back down, calculating the total distance walked and the time of reaching the hilltop. It includes a detailed solution, a list of correct and incorrect answers from various solvers, and a poetic rendition by Simple Susan and Money Spinner.

## Themes in this chapter

### Mathematical Reasoning

The chapter focuses on solving a distance-rate-time problem, analyzing correct and incorrect solutions, and highlighting indeterminate equations.

### Humor and Absurdity

The author uses playful criticism of incorrect answers, such as calling out 'A Nihilist' and 'Gerty Vernon', and includes a mock-serious charge of untruthfulness against the aged knight.

### Competition and Achievement

The chapter lists solvers by correctness, praising the 'classic Nine' who solved the whole problem, and includes a class list of successful solvers.

## Character check-ins

### Simple Susan

Submitted a joint answer with Money Spinner, solved the problem correctly, and contributed a poetic solution.

### Mimi

Submitted a joint answer with Simple Susan as Money Spinner, solved the problem correctly.

### Blithe

Solved the problem correctly and made an ingenious addition to the problem.

### Vis Inertiæ

Listed among the partially correct solvers, did not attempt the second part.

### Rose

Solved the problem correctly, though did not explicitly state the hilltop time range.

## Key lines

> Two thirds at three, one third at six, If rightly reckoned o’er, Will make one whole at four—the tale Is tangled now no more.

If you correctly calculate two-thirds of the time at 3 mph and one-third at 6 mph, the average speed becomes 4 mph, and the puzzle is solved.

_This summarizes the key insight that the average speed on the hill is 4 mph, matching the level ground speed._

> For whether long or short the time Upon the hill they spent, Two thirds were passed in going up, One third in the descent.

Regardless of how long they spent on the hill, two-thirds of that time was spent climbing up and one-third coming down.

_This explains the time proportion derived from the speeds of 3 mph up and 6 mph down._

## Links

- HTML: https://www.betterreads.online/discover/a_tangled_tale_se/chapters/answers-to-knot-i
- Book: https://www.betterreads.online/discover/a_tangled_tale_se
- All chapters: https://www.betterreads.online/discover/a_tangled_tale_se/chapters