Respuesta :
Total driving time =24
Mom drove =75 mile per hours
Dad drove = 60 miles per hours
Total distance =1710
Let
[tex]\begin{gathered} \text{ mom driving time =}^{}t_1 \\ \text{dad driviving time=}^{}t_2 \\ \text{Mom driving distance =}x \\ \text{ So dad driving distance=}^{}1710-x \end{gathered}[/tex]Total time:
[tex]t_1+t_2=24[/tex]Formula:
[tex]\text{ Spe}ed=\frac{\text{ Distance}}{\text{ Time}}[/tex]For Ava's mom:
[tex]\begin{gathered} \text{Speed}=\frac{\text{ Distance}}{\text{ time}} \\ 75=\frac{x}{t_1} \\ x=75t_1^{} \end{gathered}[/tex]For Ava's dad:
[tex]\begin{gathered} \text{ Spe}ed=\frac{\text{ Distance}}{\text{ Time}} \\ 60=\frac{1710-x}{t_2} \\ 60t_2=1710-x \\ x=1710-60t_2 \end{gathered}[/tex]Put the value of "x" then:
[tex]\begin{gathered} x=75t_1 \\ x=1710-60t_2 \\ so\colon \\ 75t_1=1710-60t_2 \\ 75t_1+60t_2=1710 \\ 15(5t_1+4t_2)=15\times114 \\ 5t_1+4t_2=114 \end{gathered}[/tex]Solve the both eq then:
[tex]\begin{gathered} t_1+t_2=24 \\ 4t_1+4t_2=96 \\ 5t_1+4t_2=114 \\ \text{then:} \\ 5t_1-4t_1+4t_2-4t_2=114-96 \\ t_1=18 \\ \end{gathered}[/tex]So Ava's mom drive 18 hours
[tex]\begin{gathered} t_1+t_2=24 \\ 18+t_2=24 \\ t_2=24-18 \\ t_2=6 \end{gathered}[/tex]Ava's dad driving 6 houras
