Lewis Carroll posed the following problem:
Two travelers spent from 2 o’clock until 9 walking along a level road up a hill and home again; their pace on the level being $x$ miles per hour, uphill $y$ mph, and downhill $2y$ mph. Find the distance walked.
In Carroll’s formulation $x$ and $y$ were given integers. Making use of the additional assumption that the original problem was solvable, find the distance walked.