Answer: [tex]204.8\ miles[/tex]
Explanation:
Remember that:
[tex]V=\frac{d}{t}[/tex]
Where "V" is the speed, "d" is the distance and "t" is the time.
You are are driving home from school steadily at 65 miles per hour for 130 miles, then we can find the driving time at 65 miles per hour:
[tex]V_1=\frac{d_1}{t_1}\\\\65\ \frac{mi}{h}=\frac{130\ mi}{t}\\\\t_1=\frac{130\ mi}{65\ \frac{mi}{h}}\\\\t_1=2\ h[/tex]
You slow down to 55 miles per hour and you arrive home after driving 3 hours and 22 minutes, then we need to find the driving time at 55 miles per hour. But first you need to convert 22 minutes to hours:
[tex](22\ min)(\frac{1\ h}{60\ min})=0.36\ h[/tex]
Since the total time is:
[tex]t_{total}=t_1+t_2[/tex]
We can calculate [tex]t_2[/tex]:
[tex]t_2=t_{total}-t_1\\\\t_2=(3\ h+0.36\ h)-2\ h\\\\t_2=1.36\ h[/tex]
In order to calculate the distance from that point (where you slow down to 55 iles per hour) to your home, we need to solve for [tex]d_2[/tex] from the following formula and substitute values:
[tex]V_2=\frac{d_2}{t_2}\\\\V_2*t_2=d_2\\\\d_2=(55\ \frac{mi}{h})(1.36\ h)\\\\d_2=74.8\ mi[/tex]
Therefore, the distance between your hometown and your school is:
[tex]d_{total}=d_1+d_2\\\\d_{total}=130\ mi+74.8\ mi\\\\d_{total}=204.8\ mi[/tex]
