Data:
In 2 1/14 x hours traveled in a speed of 140 miles per hous
In 3 hours traveled in a sped of (2x-3) miles per hour
The given data is the speed of the train and the time. The next formula is the general equation for the speed:
[tex]s=\frac{d}{t}[/tex]
s is the speed, d is the distanc and t is the time. As you need to find the distance you can solve this equation for d:
[tex]d=s\cdot t[/tex]
In the first part:
[tex]\begin{gathered} s=140\frac{mil}{h} \\ \\ t=2\frac{1}{14}xh \end{gathered}[/tex]
Then, the distance in this first part is:
[tex]\begin{gathered} d=140\frac{mil}{h}\cdot2\frac{1}{14}xh \\ \\ d=290x \end{gathered}[/tex]
Second part:
[tex]\begin{gathered} s=(2x-3)\frac{mil}{h} \\ \\ t=3h \end{gathered}[/tex]
The distance in the seond part is:
[tex]\begin{gathered} d=(2x-3)\frac{mil}{h}\cdot3h \\ \\ d=6x-9 \end{gathered}[/tex]
Then, the total distance traveled is the sum of the distance in first and second part:
[tex]\begin{gathered} d_T=290x+6x-9 \\ \\ d_T=296x-9 \end{gathered}[/tex]
