We are given the following information
After a while they stopped for gas.
Then they traveled 58 3/4 miles and stopped for lunch.
After lunch, they traveled tripled their distance before stopping for the night.
Their total distance was 381 miles.
Let x be the distance they travel before their first stop for gas.
So, the equation must be 3 times the distance x plus 58 3/4 miles and it must be equal to the total distance they traveled.
[tex]3(x+58\frac{3}{4})=381[/tex]Now, let us solve the above equation for x.
Divide both sides of the equation by 3.
[tex]\begin{gathered} \frac{3(x+58\frac{2}{4})}{3}=\frac{381}{3} \\ x+58\frac{3}{4}=127 \end{gathered}[/tex]Now, subtract 58 3/4 from both sides of the equation.
[tex]\begin{gathered} x+58\frac{3}{4}-58\frac{3}{4}=127-58\frac{3}{4} \\ x=68\frac{1}{4}\;miles \end{gathered}[/tex]Therefore, the distance they travel before their first stop for gas is 68 1/4 miles.
