Respuesta :
6 miles per hour
Explanation
Step 1
Let
x,the speed when she walks
then
2x is the speed when she jogs
total distance= 7+1= 8 miles
time joggin= time1
time walking=time2
total time = 1.5 hours
time1+time2 = 1.5
for the first 7 miles
[tex]\begin{gathered} \text{speed(x)}=\frac{dis\tan ce\text{ }}{\text{time}} \\ \text{for the first 7 miles}(\text{joggin)} \\ \text{speed}=\frac{7\text{ miles}}{\text{time}1} \\ 2x=\frac{7}{\text{time 1}}\text{ equation(1)} \\ \\ \end{gathered}[/tex]for the last mile
[tex]\begin{gathered} x=\frac{1\text{ miles}}{\text{time2}} \\ x=\frac{1}{\text{time}2}\text{ Equation (2)} \end{gathered}[/tex]Step 2
the total time is 1.5
[tex]\text{time 1+time2=1.5 equation (3)}[/tex]using equation (1) ,(2) and (3) find time 1 and time 2
a) replace the value for x from equation (2) in equation(1)
[tex]\begin{gathered} 2(\frac{1}{\text{time}2})=\frac{7}{\text{time 1}} \\ \\ \frac{2}{\text{time}2}=\frac{7}{\text{time 1}} \\ \text{time}1=\frac{7\cdot time2}{2}\text{ Equation(4)} \end{gathered}[/tex]replace this value inequation (3)
[tex]\begin{gathered} \text{time 1+time2=1.5 equation (3)} \\ \frac{7\cdot time2}{2}\text{+time2=1.5 } \\ \text{time}2(\frac{7}{2}+1)=1.5 \\ \text{time}2(4.5)=1.5 \\ \text{time}2\text{ = }\frac{1.5}{4.5} \\ \text{time}2=0.33\text{ Hous} \end{gathered}[/tex]replace this value in equation (3) to find time 1
[tex]\begin{gathered} \text{time 1+time2=1.5} \\ \text{time 1= 1.5-time2} \\ \text{time}1\text{ =1.5-0.33} \\ \text{time}1=1.16666\text{ hours} \end{gathered}[/tex]Step 3
finally the average joggin speed is
[tex]\text{average speed= }\frac{dis\tan ce}{\text{time}}=\frac{7\text{ miles}}{1.66\text{ hours}}=6\text{ miles per hour}[/tex]I hope this helps you
