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A boy rode his bicycle Northward, then turned left and rode 1 km and again turned left and rode 2 km. He found himself 1 km west of his starting point. How far did he ride northward initially?
- a)1 km
- b)2 km
- c)3 km
- d)5 km
Correct answer is option 'B'. Can you explain this answer?
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A boy rode his bicycle Northward, then turned left and rode 1 km and a...
The boy rode 2 km. Northward.
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A boy rode his bicycle Northward, then turned left and rode 1 km and a...
Given:
- A boy rode his bicycle Northward
- He turned left and rode 1 km
- He turned left and rode 2 km
- He found himself 1 km west of his starting point
To find: How far did he ride northward initially?
Solution:
Let's assume the initial distance he rode northward be 'x' km.
After taking the first left turn, he rode 1 km towards the west.
After taking the second left turn, he rode 2 km towards the south.
So, the net distance traveled towards the north would be x - 2 km.
Also, he found himself 1 km west of his starting point.
This means that the net distance traveled towards the east would be x - 1 km.
Using Pythagoras theorem, we can calculate the distance traveled by the boy.
Distance = √[(Net distance towards North)^2 + (Net distance towards East)^2]
√[(x - 2)^2 + (x - 1)^2] = x√2
Squaring both sides of the equation, we get:
(x - 2)^2 + (x - 1)^2 = 2x^2
x^2 - 6x + 5 = 0
(x - 5)(x - 1) = 0
x = 5 or x = 1
Since the boy rode towards the north initially, the value of x cannot be 1 km.
Therefore, the boy rode 2 km towards the west and 2 km towards the south, which means he rode 2 km towards the north initially.
Hence, the correct answer is option 'B' (2 km).
- A boy rode his bicycle Northward
- He turned left and rode 1 km
- He turned left and rode 2 km
- He found himself 1 km west of his starting point
To find: How far did he ride northward initially?
Solution:
Let's assume the initial distance he rode northward be 'x' km.
After taking the first left turn, he rode 1 km towards the west.
After taking the second left turn, he rode 2 km towards the south.
So, the net distance traveled towards the north would be x - 2 km.
Also, he found himself 1 km west of his starting point.
This means that the net distance traveled towards the east would be x - 1 km.
Using Pythagoras theorem, we can calculate the distance traveled by the boy.
Distance = √[(Net distance towards North)^2 + (Net distance towards East)^2]
√[(x - 2)^2 + (x - 1)^2] = x√2
Squaring both sides of the equation, we get:
(x - 2)^2 + (x - 1)^2 = 2x^2
x^2 - 6x + 5 = 0
(x - 5)(x - 1) = 0
x = 5 or x = 1
Since the boy rode towards the north initially, the value of x cannot be 1 km.
Therefore, the boy rode 2 km towards the west and 2 km towards the south, which means he rode 2 km towards the north initially.
Hence, the correct answer is option 'B' (2 km).
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