Respuesta :
Let's use the variable x to represent Jason's speed and the variable y to represent Roger's speed.
If Jason can run 4 miles per hour faster than Roger, we can write the following equation:
[tex]x=4+y[/tex]For the same time running, Jason runs 30 miles and Roger runs 18 miles, so we have:
[tex]\begin{gathered} \text{distance}=\text{speed}\cdot\text{time} \\ 30=x\cdot t \\ t=\frac{30}{x} \\ \\ 18=y\cdot t \\ t=\frac{18}{y} \\ \\ \frac{30}{x}=\frac{18}{y} \end{gathered}[/tex]Using the value of x from the first equation, we have:
[tex]\begin{gathered} \frac{30}{y+4}=\frac{18}{y} \\ 30\cdot y=18\cdot(y+4) \\ 30y=18y+72 \\ 30y-18y=72 \\ 12y=72 \\ y=\frac{72}{12} \\ y=6 \end{gathered}[/tex]Therefore Roger's speed is 6 miles per hour.
