Answer:
Ana and Larissa will not arrive in less than 2 hours
Step-by-step explanation:
we have
On a map, a trailhead is located at (5,3) and a turnaround point is located at (15, 6)
step 1
Find the distance between a trailhead point and a a turnaround point
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
substitute the values
[tex]d=\sqrt{(6-3)^{2}+(15-5)^{2}}[/tex]
[tex]d=\sqrt{(3)^{2}+(10)^{2}}[/tex]
[tex]d=\sqrt{109}=10.44\ units[/tex]
Remember that each units on the map represents 1 km
so
[tex]d=10.44\ km[/tex]
step 2
Find the time
The speed is equal to the ratio between the distance and the time
Let
s ----> the speed
d ----> the distance in km
t ---> the time in hours
[tex]s=\frac{d}{t}[/tex]
we have
[tex]d=10.44\ km[/tex]
[tex]s=4.5\ km/h[/tex]
substitute in the formula and solve for t
[tex]4.5=\frac{10.44}{t}[/tex]
[tex]t=\frac{10.44}{4.5}[/tex]
[tex]t=2.32\ hours}[/tex]
[tex]2.32\ h > 2\ h[/tex]
therefore
Ana and Larissa will not arrive in less than 2 hours
