Question 658559
Let r be the motorists rate on the mountain roads.  Then his rate on country roads is 3r.

So is time on country roads is 150/3r, and his time on mountain roads is 50/r.  The sum of these two times is 5 hours:
{{{150/(3*r) + 50/r = 5}}}
{{{150/(3*r) + (3/3)*(50/r) = 5}}}
{{{150/(3*r) + 150/(3*r) = 5}}}
{{{(150+150)/(3*r) = 5}}}
{{{300/(3*r) = 5)}}}
{{{100/r = 5}}}
Cross-multiplying:
{{{5*r = 100}}}
{{{r = 20}}}
The motorist's rate on mountain roads was 20 mph and his rate on country roads was 60 mph.