Sam Loyd's Jack and Jill Puzzle - Solution

The Puzzle:

Sam Loyd's Jack and Jill Puzzle
Here is a pretty puzzle from Mother Goose's story of Jack and Jill's race for a pail of water.

The distance to the top of the hill was 440 yards, which is just a quarter of a mile.

Jack got to the top first and was 20 yards on the return trip when he met Jill whom he beat home by half a minute.

The record of the race is complicated by the runners being able to run down hill one-half again faster than they ran up, so you are asked to figure out Jack's time for the half mile run.

Our Solution:

It is clear that 60 feet down hill is equal to 40 feet up hill, we see that Jack accomplished the equivalent of 1,360 feet and Jill but 1,260 when they met, which shows their speeds to be in the proportion of 63 to 68.

As Jack beat Jill by 5/63 of his time, which was equal to half a minute, 1/63 of his time is equal to 6 seconds, and his whole time, therefore, would be 6 minutes and 18 seconds, which is the correct answer to the problem of Jack's speed for the half-mile run.

Puzzle Author: Loyd, Sam

See this puzzle without solution
Discuss this puzzle at the Math is Fun Forum