# From Bixley to Quixley

Here is a nice problem that occurred to me during a trip from Bixley to Quixley that I did on the back of a mule.

I asked don Pedro, the native guide who walked in front of me taking my mule from the reins, if my ride could move to another step.

He said yes, but it was much slower, so I continued my journey at a uniform speed. To stimulate Don Pedro, responsible for my sole driving power, I told him that on the way, we would go to Pixley to have a drink and from that moment he could not think of anything else than Pixley.

When we had been traveling for forty minutes, I asked him how far we had traveled, Don Pedro replied: "Half the distance to Pixley."

When we had covered seven more miles I asked: "How far is it to Quixley?" He replied as before: "Half the distance left to Pixley."

We arrived at Quixley in another hour of travel, which leads me to ask you to determine the distance between Bixley and Quixley.

#### Solution

Let's suppose X be the point (between Bixley and Pixley) at which the first question is asked Y the point (between Pixley and Quixley) where the second question is asked.

The distance from X to Y We are told that it is 7 miles. As the distance from X to Pixley is 2/3 of the distance between Bixley and Pixley and the distance from Y Pixley is 2/3 of the distance between Pixley and Bixley, it follows that the distance between X and Y that is 7 miles, it is 2/3 of the total distance. This makes the total distance 10 and a half miles.