A horse chases a pony 2 hours after the pony runs. Horse takes 3 hours to reach the pony. If the average speed of the horse is 81Kmph.Then what is the average speed of the pony?a)46.4 b)51 c)53.4 d)48.6Correct answer is option 'D'. Can you explain this answer?

Question

A horse chases a pony 2 hours after the pony runs. Horse takes 3 hours to reach the pony. If the average speed of the horse is 81Kmph.Then what is the average speed of the pony?a)46.4            b)51       c)53.4            d)48.6Correct answer is option 'D'. Can you explain this answer?

Answer

Given information:
- A horse chases a pony 2 hours after the pony starts running.
- The horse takes 3 hours to reach the pony.
- The average speed of the horse is 81 km/h.

To find:
The average speed of the pony.

Assumptions:
- The horse and the pony run at a constant speed during the entire duration of the chase.
- The distance between the horse and the pony remains constant during the chase.

Solution:

Step 1: Understanding the problem
Let's assume the distance between the horse and the pony when the horse starts chasing is 'd' km. We need to find the average speed of the pony.

Step 2: Analyzing the horse's chase
- The horse starts chasing the pony 2 hours after the pony starts running.
- It takes the horse 3 hours to reach the pony.
- Therefore, the total time the horse takes to chase the pony is 3 + 2 = 5 hours.
- During this time, the horse covers the distance 'd' km.

Step 3: Calculating the distance
- We know that the average speed is calculated by dividing the total distance by the total time.
- Therefore, the distance covered by the horse is given by the formula: distance = speed × time.
- Using the given information, the distance covered by the horse is 81 km/h × 5 h = 405 km.

Step 4: Calculating the average speed of the pony
- We know that the distance between the horse and the pony remains constant during the chase.
- Therefore, the distance covered by the pony is 405 km as well.
- The time taken by the pony to cover this distance is 2 hours (since the horse starts chasing 2 hours after the pony starts running).
- Therefore, the average speed of the pony is given by the formula: speed = distance / time = 405 km / 2 h = 202.5 km/h.

Step 5: Converting the speed to km/h
- The average speed of the pony is calculated to be 202.5 km/h, but we need to convert it to km/h.
- To convert km/h to km/h, we multiply the value by 1.
- Therefore, the average speed of the pony is 202.5 km/h × 1 = 202.5 km/h.

Step 6: Rounding the answer
- The average speed of the pony is 202.5 km/h.
- Rounding this value to the nearest unit gives us the answer: 203 km/h.

Final answer:
The average speed of the pony is approximately 203 km/h.

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