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The speed of the engine of a train with no wagon attached to it is 64 km/h, and the reduction in speed is directly proportional to the square root of the number of wagons attached. When 16 compartments are attached the speed of the train is 32 km/h. Find the maximum number of wagons that can be pulled by the engine before it stops.
  • a)
    32
  • b)
    48
  • c)
    36
  • d)
    64
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
The speed of the engine of a train with no wagon attached to it is 64 ...
Problem Analysis:
- The speed of the train with no wagon attached = 64 km/h
- The reduction in speed is directly proportional to the square root of the number of wagons attached
- When 16 compartments are attached, the speed of the train is 32 km/h
- We need to find the maximum number of wagons that can be pulled by the engine before it stops

Solution:
1. Let's assume that the maximum number of wagons that can be pulled by the engine is 'x'
2. Using the given information, we can form the following equation:
Speed with x wagons = 64 / sqrt(x)
Speed with 16 wagons = 32 km/h
3. Using the above equations, we can write:
64 / sqrt(x) = 32 / sqrt(16)
=> 64 / sqrt(x) = 8
=> sqrt(x) = 64 / 8
=> sqrt(x) = 8
=> x = 8^2
=> x = 64
4. Therefore, the maximum number of wagons that can be pulled by the engine before it stops is 64.

Final Answer: The correct option is 'D'
Community Answer
The speed of the engine of a train with no wagon attached to it is 64 ...
64 is correct answer
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The speed of the engine of a train with no wagon attached to it is 64 km/h, and the reduction in speed is directly proportional to the square root of the number of wagons attached. When 16 compartments are attached the speed of the train is 32 km/h. Find the maximum number of wagons that can be pulled by the engine before it stops.a)32b)48c)36d)64Correct answer is option 'D'. Can you explain this answer?
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