Question 757155
x = rate of travel to parents, y = rate of travel home

On his way there his average speed was 20 mph faster than on his way home.

{{{x = y + 20}}}

Jon spent 8 hours driving

Time equals distance divided by rate.

t = d/r

{{{192/x + 192/y = 8}}} time for the trip to parents plus time to get home equals 8 hours

Now substituting y+20 in for x
{{{192/(y+20) + 192/y = 8}}}
{{{192y + 192(y+20) = 8y(y+20)}}}
{{{192y + 192y + 3840 = 8y^2 + 160y}}}
{{{8y^2 - 224y - 3840 = 0}}}
{{{y^2 - 28y - 480 = 0}}}
{{{(y-20)(y+12)=0}}}
y = 20
x = y + 20 = 20 + 20 = 40