Skip to main contentSkip to solution

A man drives 20 km towards the East and turns to the right-hand side and takes a drive of another 3 km. He then drives towards the West (turning to his right) another 3 km. He then turns to his left and walks another 2 km. Afterward, he turns to his right and travels 17 km. How far is he from his starting point?

Solution

✅ Correct Option: 2

Setting up a coordinate system with the starting point at the origin (0, 0), where East is the positive x-direction and North is the positive y-direction.

Starting position: (0, 0), initially facing East


Drives 20 km towards the East:

Position: (20, 0)

Direction: East


Turns to the right and drives 3 km:

Turning right from East means facing South

Position: (20, -3)

Direction: South


Turns to his right (towards West) and drives 3 km:

Turning right from South means facing West

Position: (20 - 3, -3) = (17, -3)

Direction: West


Turns to his left and walks 2 km:

Turning left from West means facing South

Position: (17, -3 - 2) = (17, -5)

Direction: South


Turns to his right and travels 17 km:

Turning right from South means facing West

Position: (17 - 17, -5) = (0, -5)

Direction: West


Distance from starting point (0, 0) to final position (0, -5):

d=(0−0)2+(−5−0)2d = \sqrt{(0-0)^2 + (-5-0)^2}

d=0+25d = \sqrt{0 + 25}

d=5d = 5 km

Therefore, he is 5 km from his starting point.

Keyboard Shortcuts

  • Left arrow: Previous question
  • Right arrow: Next question
  • S key: Jump to solution
  • Q key: Jump to question