Question

- 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.

Answer 1

Ana and Larissa will not arrive in less than 2 hours

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

`d=\sqrt{(y2-y1)^(2)+(x2-x1)^(2)}`

substitute the values

`d=\sqrt{(6-3)^(2)+(15-5)^(2)}`

`d=\sqrt{(3)^(2)+(10)^(2)}`

`d=√(109)=10.44\ units`

Remember that each units on the map represents 1 km

so

`d=10.44\ km`

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

`s=(d)/(t)`

we have

`d=10.44\ km`

`s=4.5\ km/h`

substitute in the formula and solve for t

`4.5=(10.44)/(t)`

`t=(10.44)/(4.5)`

`t=2.32\ hours}`

`2.32\ h > 2\ h`

therefore

Ana and Larissa will not arrive in less than 2 hours