Question 1005457
{{{x}}}= average speed of the bicycle, in mph.
So,
{{{x+35.8}}}= average speed of the car, in mph,
{{{4.5x}}}= distance covered by the bicycle in 4.5 hours, in miles,
{{{4.5(x+35.8)}}}= distance covered by the car in 4.5 hours, in miles, and
{{{4.5x+4.5(x+35.8)}}}= total distance covered by the bicycle and car in 4.5 hours, in miles.
Since after 4.5 hours the whole {{{279}}} miles of road across the state had been covered between bicycle and car,
{{{4.5x+4.5(x+35.8)=279}}} is our equation.


Solving:
{{{4.5x+4.5(x+35.8)=279}}}
{{{4.5x+4.5x+4.5*35.8=279}}}
{{{9x+161.1=279}}}
{{{9x=279-161.1}}}
{{{9x=117.9}}}
{{{x=117.9/9}}}
{{{x=13.1}}}
{{{x+35.8=13.1+35.8}}}
{{{x+35.8=48.9}}}