A man starts from point A and travels 3 km towards the east to reach B and then turns left and travels thrice the distance to reach another point C. From there he again turns left and travels five times the distance he covered between A and B and reaches his destination D. What is the shortest distance between the starting point and his destination?
15 km
Let A be the origin (0, 0). Travelling 3 km east reaches B at (3, 0).
Turning left from east means facing north; travelling thrice the AB distance, that is 9 km, reaches C at (3, 9).
Turning left again from north means facing west; travelling five times the AB distance, that is 15 km, reaches D at \(3 - 15 = -12\), so D is at (-12, 9).
The shortest distance AD is \(\sqrt{(-12-0)^2 + (9-0)^2} = \sqrt{144 + 81} = \sqrt{225} = 15\) km.
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