# The Casey cow puzzle

Here is another railway puzzle that illustrates a beautiful mathematical principle and at the same time shows us a moral.

"I am pleased to see that many cows have more common sense than some men."
Casey thought philosophically.

Casey was on the railroad bridge the other day quietly contemplating the water when suddenly he saw the light of the express that was just twice the length of the bridge beyond the other end and was approaching ninety miles per hour.

At that time, she didn't waste a forty-eleventh millionth part of a second in speculation, since she couldn't swim, she had to get to the mainland before the train rolled over her so she ran to the advancing train and ended up being saved from being overwhelmed by the narrow margin of one foot away, while, if she had followed the human instinct and had run away in the opposite direction to the train, three inches of her ass would have been rolled on the bridge by the train!

It is a nice problem to determine the speed of the cow and the length of the bridge knowing that the cow is five feet from the center of the bridge in the direction from which the train is coming.

Can you calculate it?

Summarizing:

• 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 to the train she escapes from being hit by one foot but if the cow runs in the opposite direction, the train hits her when she still has three inches of her butt inside the bridge.

Assuming it doesn't take any time for the cow to turn around calculate:

What is the length of the bridge? And at what speed does the cow move?

For those who are not familiar with the English measurement system it is necessary to know that:

• One foot is 12 inches.
• A yard is 3 feet
• One mile equals 5280 feet

#### Solution

The bridge measures 48 feet and the cow runs at 18 miles per hour.

Since the train travels twice the length of the bridge minus one foot while the cow travels the length of half a bridge minus 5 feet and instead, moving in the opposite direction the train would travel three times the length of the bridge minus three inches while the cow would advance the length of half a bridge plus 4 feet and 9 inches we deduce that, in the time that the train would advance 5 times the length of the bridge minus 15 inches the cow would advance once the length of the bridge minus three inches.

This means that the train is exactly 5 times faster than the cow and also that twice the length of the bridge minus one foot is equal to two and a half times the length of the bridge minus 25 feet.

Therefore, half the length of the bridge is equal to 24 feet, then the total length will be 48 feet.

Since the train is moving 5 times faster than the cow, at 90 miles per hour, the speed of the cow will be 18 miles per hour.