Problem

"Walk-and-Tie" Method:

Years ago when people traveled on horseback, they might find themselves away from home without enough money for the return trip. A common solution for a pair of people with two horses was to sell one horse and take turns riding the other one home. Since a horse walks faster than a person, one person rode ahead foe a while, tied up the horse, and continued walking toward home.

The second person would reach the point where the horse was tied and begin riding until he or she caught up with the first person. They would repeat this until they get home.

Suppose a horse travels five miles per hour and two people walk three miles per hour. How long will it take to make a twenty-mile trip if the "walk-and-tie" method is used?

Answer

Assuming, that the people using the "walk-and-tie" method, want to take the quickest way home (they arrive at their home at the same time), it will take Five hours, and four minutes. I got this answer by:

1 person - walks 3 miles an hour:

(60 minutes / 3 miles an hour = 20 minutes)

Going one mile takes 20 minutes.

1 horse - walks 5 miles an hour:

(60 minutes / 5 miles an hour = 12 minutes)

Going one mile takes 12 minutes.

The first person rides the horse 1 mile (12 minutes)

The second person walks 1 mile (20 minutes)

The time it took the second person 1 mile (20 minutes) subtracted from the time it takes the first person (on the horse) to walk 1 mile (12 minutes) equals how long the horse isn’t moving (8 minutes).

The horse is constantly being rode, accept the 8 minutes the horse isn’t moving.

In other words, the horse isn’t moving for 8/20 of the time (or a person will be moving for 8/20 of the time)

The rest of the time (12/20) the horse must be moving.

With this information, we know that the horse is moving for 12/20 of the time.

A person is walking for 8/20 of the time:

(8/20 * 20 miles = 8 miles)

(8 miles * 20 minutes = 160 minutes)

A total of 160 minutes of walking without horse-riding

A horse is riding for 12/20 of the time:

(12/20 * 20 miles = 12 miles)

(12 miles * 12 minutes = 144 minutes)