Mindy's time: 5 h
Kelly's time: 6 h
The distance is the same for both of them, then
[tex]\begin{gathered} d=r_mt_m\text{ for Mandy} \\ d=r_kt_k\text{ for Kelly} \end{gathered}[/tex][tex]\begin{gathered} r_mt_m=r_kt_k \\ r_m\times5=(r_m-10)\times6 \\ r_m\times5=6r_m-60 \\ r_m=60\text{ mi/h} \end{gathered}[/tex]for Kelly
[tex]\begin{gathered} r_k=r_m-10 \\ r_k=60-10 \\ r_k=50\text{ mi/h} \end{gathered}[/tex]so
[tex]\begin{gathered} d=r_mt_m \\ d=60\times5 \\ d=300\text{ }mi\text{ for Mandy} \end{gathered}[/tex][tex]\begin{gathered} d=r_kt_k \\ d=50\times6 \\ d=300\text{ mi for Kelly} \end{gathered}[/tex]Both ways of finding d agree, so distance is 300 miles