A man travels 3 miles, turns left and travels 6 miles, then left again and travels 8 miles. How far is he from the starting point? a. 4 b. 7 c. 5 d. 9. Give reasons
Answers
Given : A man travels 3 miles, turns left and travels 6 miles, then left again and travels 8 miles.
To Find : How far is he from the starting point?
a. 4 b. 7 c. 5 d. 9.
Solution:
Turning left two time is equivalent to U turn (reverse direction)
A man travels 3 miles
turns left and travels 6 miles
, then left again and travels 8 miles => ( 8 miles are in opposite direction to 3 miles )
Hence 6 miles in one direction and ( 3 - 8) = - 5 miles in other direction and both are perpendicular
Hence Distance from starting point = √(-5)² + 6²
= √25 + 36
= √61
= 7.8 miles
None of the given option matches.
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Answer :-
Since it is not clear the man starts travelling in which direction , let us assume that he travel east.
so,
→ 3 miles east from starting point . (AB = 3 miles.)
A ---------- B .
now, he turns left and travel 6 miles .
→ East to left = North = 6 miles (BC = 6 miles .)
C
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A ---------- B
now, again he turns left and travel 8 miles .
→ North to left = west = 8 miles . (CD = 8 miles .)
D--------------------C
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A ---------- B
then,
→ AD = √{(DC - AB)² + CB²} (By pythagoras theorem.)
→ AD = √{(8 - 3)² + (6)²}
→ AD = √(5² + 6²)
→ AD = √(25 + 36)
→ AD = √61
→ AD ≈ 7.81 miles (Ans.)
therefore none of the option is correct.
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