As valuable knowledge demonstrates, mind improvement can be achieved from current events that can happen to a gentleman during a summer excursion, Fatie Willie murmured during one of his bright moments.

I remember a casual encounter with Tired Tim on a railroad track where we first met and we exchanged a fraternal greeting. Apparently they recommended a change of air to the city of Joytown at the same time that I was convinced that it would be better for my health to go to Pleasantville. This is how we first met ten miles from Joytown.

We fraternize fair and sufficient time to become colleagues, exchange our experiences and then head to our respective destinations.

It turned out that both cities were overrated and full of people of doubtful tasting that were to be waste of times gone by. The acceptance of the recommendation of the police who very carefully recommended both gentlemen to return by the same route from where we had come made us begin our respective return trips at the same time.

That is why, as shown in the drawing, I agreed again with my old acquaintance at a point twelve miles from Pleasantville, but I bet a beer that from the data provided can not **find out the distance in miles between Joytown and Pleasantville**.

Of course, it is assumed that each of the pedestrians maintained their own gear both when going and returning from one city to the other.

#### Solution

The answer to this problem can be obtained by a simple addition, subtraction and a little common sense as follows:

When they first met Fatigued Willie was ten miles from Joytown, so the sum of the distances traveled by both corresponded to the distance between the two cities.

When they met for the second time their combined trips amounted to three times the distance between both cities. Fatigued Willie, who had traveled ten miles at his first meeting, must therefore have traveled 30 miles until his second meeting.

In this second encounter Tired Willie had walked ten miles from Joytown to his encounter with Tim, the distance from the first sign to Pleasantville and 12 miles from Pleasantville to the sign in the second image.

We have shown that at that time the combined distance traveled by both was 30 miles. Also that Fatigued Willie walked 10 miles, 12 miles and the distance between the first image signal to Pleasantville.

Therefore the distance corresponding to this section can be obtained by subtracting the 22 miles from the total 30 miles which gives us the 8 miles that Willie had to travel to complete his trip to Pleasantville after having walked the 10 miles to the first sign . Thus, **the distance between cities must be 18 miles**.

The question of who Willie is and who Tim is cannot be answered from the image, so we can baptize them as we want without affecting the puzzle.