Question

On a map, a trailhead is located at (13,2) and a turnaround point is located at (-2,8). 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 5.5 km/h, will they make it to the trailhead in less than 3 hours? (Yes/No)

a) Yes
b) No

Answer 1

By calculating the distance between the trailhead and the turnaround point to be approximately 16.16 km and dividing the distance by the average walking speed, we determine Ana and Larissa will make it to the trailhead in approximately 2.94 hours. Therefore, they will reach their destination in less than 3 hours.

Step-by-step explanation:

First, we need to calculate the distance between the points (13,2) and (-2,8) using the distance formula:

Distance = √((x2 - x1)^2 + (y2 - y1)^2)

Distance = √((-2 - 13)^2 + (8 - 2)^2)

Distance = √((-15)^2 + (6)^2)

Distance = √(225 + 36)

Distance = √(261)

Distance ≅ 16.16 km

To find out if Ana and Larissa can make it to the trailhead in less than 3 hours, we divide the distance by their walking speed.

Time = Distance / Speed

Time = 16.16 km / 5.5 km/h

Time ≅ 2.94 hours

Since 2.94 hours is less than 3 hours, the answer is (a) Yes, Ana and Larissa will make it to the trailhead in less than 3 hours.