MATH SOLVE

3 months ago

Q:
# - On a map, a trailhead is located at (5,3) and aturnaround point is located at (15, 6). Each uniton the map represents 1 km. Ana and Larissastart at the turnaround point and walk directlytoward the trailhead. If they walk at an averagespeed of 4.5 km/h, will they make it to thetrailhead in less than 2 hours? Support youranswer.

Accepted Solution

A:

Answer:Ana and Larissa will not arrive in less than 2 hoursStep-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 1Find the distance between a trailhead point and a a turnaround pointthe 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 kmso[tex]d=10.44\ km[/tex]
step 2Find the timeThe speed is equal to the ratio between the distance and the timeLets ----> the speedd ----> the distance in kmt ---> 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]thereforeAna and Larissa will not arrive in less than 2 hours