Question

1. on a map, a trailhead is located at (5,3) and a turnaround point is located at (15,6). each unit on the map represents 1 km. ana and larissa start at the turnaround point and walk directly toward the trailhead. if they walk at an average speed of 4.5 km/h, will they make it to the trailhead in less than 2 hours? support your answer.

Explanation:

Step1: Calculate the distance between two points

Use the distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Here, \((x_1,y_1)=(5,3)\) and \((x_2,y_2)=(15,6)\).

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Step2: Calculate the time taken

Use the formula \(t=\frac{d}{v}\), where \(v = 4.5\) km/h and \(d\approx10.44\) km.
\(t=\frac{10.44}{4.5}\approx2.32\) h

Answer:

No, they will not make it to the trailhead in less than 2 hours. Since the time taken \(t\approx2.32\) h which is greater than 2 h.