Henry Ernest Dudeney/Modern Puzzles/164 - Those Russian Cyclists Again/Solution

by : $164$

 * Those Russian Cyclists Again

Solution

 * $25$ miles.

Proof
Let $BC = a$, $AC = b$ and $AB = c$.

Let $CD = d$.

Let $AD = c_1$ and $BD = c_2$.

We have:

Then we have:

Setting $a + b + c = 60$ and $d = 12$ gives the result.

Hence 's General simply squared $60$ and divided by $2 \times \paren {60 + 12}$:


 * $c = \dfrac {60^2} {2 \times \paren {12 + 60} } = \dfrac {3600} {144} = 25$