**Solution**

A level mile takes quarter of an hour, up hill one third, down hill one sixth. Hence to go and return over the same mile, whether on the level or on the hill-side, takes half an hour. Hence in six hours they went 12 miles out and 12 miles back. If the 12 miles out had been nearly all level, they would have taken a little over 3 hours; if nearly all up hill, a little under 4. Hence three and a half hours must be within half an hour of the time taken in reaching the peak; thus, as they started at 3, they got there within half an hour of half past six.