Question

ava's family drove to disneyland for spring break. Her mom and dad shared the driving duties for a total of 24 hours. Her mom drove 75 miles per hour, and her dad drove 60 miles per hour. If they drove a total of 1,710 miles, how many hours did each person drive for?

Answer 1

Total driving time =24

Mom drove =75 mile per hours

Dad drove = 60 miles per hours

Total distance =1710

Let

`\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}`

Total time:

`t_1+t_2=24`

Formula:

`\text{ Spe}ed=\frac{\text{ Distance}}{\text{ Time}}`

For Ava's mom:

`\begin{gathered} \text{Speed}=\frac{\text{ Distance}}{\text{ time}} \\ 75=(x)/(t_1) \\ x=75t_1^{} \end{gathered}`

For Ava's dad:

`\begin{gathered} \text{ Spe}ed=\frac{\text{ Distance}}{\text{ Time}} \\ 60=(1710-x)/(t_2) \\ 60t_2=1710-x \\ x=1710-60t_2 \end{gathered}`

Put the value of "x" then:

`\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*114 \\ 5t_1+4t_2=114 \end{gathered}`

Solve the both eq then:

`\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}`

So Ava's mom drive 18 hours

`\begin{gathered} t_1+t_2=24 \\ 18+t_2=24 \\ t_2=24-18 \\ t_2=6 \end{gathered}`

Ava's dad driving 6 houras