Answer:
The distance she walks is 5 km
Step-by-step explanation:
Let
x -----> the distance in kilometers
y ----> the time in hours
we know that the speed is equal to divide the distance by the time
Average speed of 5 km/h
[tex]5=\frac{x}{y}[/tex]
[tex]y=\frac{x}{5}[/tex] -----> equation A
Average speed of 6 km/h
convert 10 minutes to hours
[tex]10\ min=10/60=1/6\ h[/tex]
[tex]6=\frac{x}{y-\frac{1}{6}}[/tex] ----> equation B
Solve the system by graphing
The solution is the intersection point both graphs
The solution is the point (5,1)
see the attached figure
therefore
The distance she walks is 5 km
Verify
Average speed of 5 km/h
[tex]y=\frac{5}{5}=1\ h=(1)*60=60\ min[/tex]
Average speed of 6 km/h
[tex]y=\frac{5}{6}\ h=\frac{5}{6}*60=50\ min[/tex]
The difference is the time she will save
[tex]60\ min-50\ min=10\ min[/tex] ----> is correct
