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A carriage driving in a fog passed a man who was walking at the rate of 3 km an hour in the same direction. He could see the carriage for 4 minutes and it was visible to him upto a distance of 100 m. What was the speed of the carriage?
  • a)
    9/2 km/h
  • b)
    11/2 km/h
  • c)
    37/2 km/h
  • d)
    13/2 km/h
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
A carriage driving in a fog passed a man who was walking at the rate ...
The distance travelled by the man in 4 min = [(3×1000)/60] ×4=200 meters
∴ distance travelled by the carriage in 4 min = (200 + 100) = 300 meters
∴ speed of the carriage = (300/4)×(60/1000) km/hour
=9/2 km/hour
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Most Upvoted Answer
A carriage driving in a fog passed a man who was walking at the rate ...
Given information:
- The man is walking at a speed of 3 km/h in the same direction as the carriage.
- The man can see the carriage for 4 minutes.
- The carriage is visible to the man up to a distance of 100 meters.

To find:
The speed of the carriage.

Assumptions:
- The fog does not affect the visibility of the carriage.
- The man maintains a constant speed of 3 km/h throughout.

Approach:
1. Convert the given information into a common unit (either km/h or m/s).
2. Calculate the relative speed of the carriage with respect to the man.
3. Use the relative speed and the time the carriage was visible to calculate the distance traveled by the carriage.
4. Use the distance traveled by the carriage and the distance at which it was visible to calculate the speed of the carriage.

Solution:
We need to convert the speed of the man to the same unit as the distance at which the carriage was visible. Converting 3 km/h to m/s:

Speed of the man = 3 km/h = 3 * (1000/3600) m/s = 5/6 m/s

Calculating Relative Speed:
The relative speed of the carriage with respect to the man can be calculated by subtracting the speed of the man from the speed of the carriage.

Relative speed = Speed of the carriage - Speed of the man

Since the man is walking in the same direction as the carriage, the relative speed will be:

Relative speed = Speed of the carriage - (5/6) m/s

Calculating Distance Traveled by the Carriage:
The distance traveled by the carriage can be calculated using the relative speed and the time the carriage was visible to the man.

Distance = Relative speed * Time

Distance = (Speed of the carriage - (5/6)) * 4 minutes

Note: Convert the time to seconds for consistency.

Distance = (Speed of the carriage - (5/6)) * 240 seconds

Calculating Speed of the Carriage:
The speed of the carriage can be calculated using the distance traveled by the carriage and the distance at which it was visible.

Distance traveled by the carriage = Speed of the carriage * Time

100 meters = Speed of the carriage * 240 seconds

Speed of the carriage = 100/240 m/s

Converting to km/h:

Speed of the carriage = (100/240) * (3600/1000) km/h

Final Answer:
Simplifying the expression:

Speed of the carriage = 15/4 km/h = 3.75 km/h

Therefore, the speed of the carriage is 3.75 km/h.

Correct Answer:
Option (A) 9/2 km/h
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A carriage driving in a fog passed a man who was walking at the rate of 3 km an hour in the same direction. He could see the carriage for 4 minutes and it was visible to him upto a distance of 100 m. What was the speed of the carriage?a)9/2 km/hb)11/2 km/hc)37/2 km/hd)13/2 km/hCorrect answer is option 'A'. Can you explain this answer?
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