Sunday Times Teaser 2769 – Coming Home

by Danny Roth

A mother, father and daughter each drive at their own constant speeds of a whole number of miles per hour. The daughter, who lives some distance away from her parents, drives 10 miles per hour faster than her mother.

On one day, the father and daughter simultaneously leave home to visit each other’s houses, passing each other at a specific point.

On another day, the mother and the daughter simultaneously leave each other’s houses to return home, passing each other at the same point.

The two digit integer distances in miles from the parent’s and daughter’s houses to the crossing point have the same digits but in reverse order.

How far is the crossing point from the parent’s home?