Puzzle of Casey's cow

Puzzle

Here is another Rail Road Puzzle, which illustrates a pretty mathematical principle and at the same time points a moral and adorns a tale which all might ponder over to advantage:

"I am satisfied that some cows have more sense than the average man." soliloquized Casey, in his philosophical way.

"My old brindle was standing on the long bridge the other day, placidly looking into the water, when she spied the lightning express, just twice the length of the bridge away from the end, coming at a ninety-mile an hour clip. Now, she did not waste the forty-eleven-millionth part of a second in idle speculation; she just made a dash towards the advancing train and saved herself by the narrow margin of one foot, whereas, if she had followed the human instinct of running away from the train, three inches of her rear would have been caught on the bridge!"

It would be a great thing if some procrastinators, who never can make up their minds one way or the other, were placed in the position of my old brindle cow, so they had to think quick!

It is a pretty problem to reckon the gait of that cow, and to tell how far she was standing from the middle of the long bridge! Can you figure it out ?"

Comment to puzzle

Actually the puzzle is not solvable as given.

Judging from the answer given the cow is five feet from the center of the bridge towards the train.

What needs to be calculated is the length of the bridge and the speed of the cow.

Puzzle in short

The cow is five feet from the center of the bridge in the direction of the train.

The train is two bridge lengths from the beginning of the bridge.

The train speed is 90 miles per hour.

If the cow runs towards the train she escapes the train by one foot.

But if the cow runs away from the train she is hit by the train when she has three inches left to safety at end of the bridge.

Assume that it takes no time for the cow to turn.

Calculate:

1. How long is the bridge?
2. How fast does the cow run?

Units

Feet and inches for the metric crowd

Solution

Answer

References

• Loyd, Sam [1914]. in Loyd, Sam, Jr.: Sam Loyd's Cyclopedia of 5000 Puzzles Tricks and Conundrums (in English). New York: Lamb Publishing company, page 10.