Question

Two friends “a” and “b” start walking from a common point. A goes $20\mathrm{km}$ towards the northeast, whereas “b” goes $15\mathrm{km}$ towards the east and then $12\mathrm{km}$ towards the north. How far are “a” and “b” from each other?

Answer 1

Step 1: Given data

a and b start walking from a common point.

a goes $20\mathrm{km}$ towards the northeast.

b goes $16\mathrm{km}$ towards the east and then $12\mathrm{km}$ towards the north.

Step 2: To find

We have to find the distance between a and b.

Step 3: Calculation

By using the given information, we get

By using the Pythagoras theorem,

$$\begin{gathered} \mathrm{Displacement}\mathrm{of}\mathrm{b}=\sqrt{{\left(16\right)}^2+{\left(12\right)}^2} \\ =\sqrt{256+144} \\ =\sqrt{400} \\ =20\mathrm{km} \end{gathered}$$

Now, a and b will meet again at the end of their voyage, and the distance between them will be:

$$\begin{gathered} =20-20 \\ =0\mathrm{km} \end{gathered}$$

Therefore, the distance between a and b is $0\mathrm{km}$.