Question

F a student drives 30 miles north, the 40 miles east, then 60 more miles north and finally 80 more miles east, exactly how far is she from her starting point? (As the crow flies.)

Answer 1

150 miles

Explanation:

The movements are represented as:

`N1 = 30miles`

`E1 = 40miles`

`N2 = 60miles`

`E2 = 80miles`

Required

Determine the distance from the starting point

The student's movement is illustrated with the attached image.

First, calculate the total distance towards North.

`N = N1 + N2`

`N = 30 + 60`

`N = 90`

Next, calculate the total distance towards East

`E = E1 + E2`

`E = 40 + 80`

`E = 120`

The total distance from the starting point is calculated using Pythagoras theorem.

`D^2 = N^2 + E^2`

`D^2 = 90^2 + 120^2`

`D^2 = 22500`

`D = \sqrt{22500`

`D = 150`