Henry Ernest Dudeney/Modern Puzzles/44 - Find the Distance/Solution

by : $44$

 * Find the Distance

Solution

 * $18$ miles.

The "absurdly simple" rule being referred to by :


 * $3$ times the distance from $A$ that they first cross minus the distance from $B$ when they cross for the second time.

Proof
Let $d$ miles be the distance between $A$ and $B$.

Let $V_J$ and $V_K$ miles per hour be the speeds of Jones and Kenward respectively.

Then we have:

For the general case, let $d_1$ and $d_2$ be the distances from $A$ and $B$ that they crossed respectively.

We have:

So the general rule is:
 * $d = 3 d_1 - d_2$