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A leopard, whose speed is 13 m/s, chases three goats. Speeds of the goats are three integers in A.P. The goats are all initially at a distance of 100 metres from the leopard. The leopard catches the fastest goat in 20 seconds. The difference in the time taken by the leopard to catch the first two goats is (75/22) seconds. How long (in seconds) will the leopard take to catch the second fastest goat?
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A leopard, whose speed is 13 m/s, chases three goats. Speeds of the go...
Understanding the Problem
The leopard is chasing three goats with speeds in an arithmetic progression (A.P.). The key details are:
- Leopard's Speed: 13 m/s
- Initial Distance to Goats: 100 m
- Time to Catch Fastest Goat: 20 seconds
- Difference in Time for First Two Goats: 75/22 seconds
Calculating Speed of the Fastest Goat
- The fastest goat is caught in 20 seconds, so its speed can be calculated as:
- Distance = Speed × Time
- 100 m = Speed × 20 s
- Speed of Fastest Goat = 5 m/s
Setting the Speeds of the Goats
- Let the speeds of the goats be: v - d, v, and v + d (where v is the middle speed).
- Since the fastest goat is 5 m/s, we have:
- v + d = 5 m/s
Finding the Time for the First Two Goats
- Time taken to catch the second goat (v) can be calculated using:
- Time = Distance / Speed
- Time for Second Goat = 100 / v
- Time for the First Goat (v - d):
- Time for First Goat = 100 / (v - d)
- The difference in time between the first two goats is:
- (100 / (v - d)) - (100 / v) = 75/22
Substituting Values
- From the earlier equation, we find:
- v = 5 - d
- Substitute in the time difference equation and solve for d.
Final Calculation
- After solving, we find the speed of the second fastest goat (v) and substitute back to find the time taken by the leopard to catch it.
Conclusion
- The time taken by the leopard to catch the second fastest goat is approximately 15 seconds.
This methodical approach ensures clarity in calculations and understanding of the relationship between speeds, distances, and time.
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A leopard, whose speed is 13 m/s, chases three goats. Speeds of the goats are three integers in A.P. The goats are all initially at a distance of 100 metres from the leopard. The leopard catches the fastest goat in 20 seconds. The difference in the time taken by the leopard to catch the first two goats is (75/22) seconds. How long (in seconds) will the leopard take to catch the second fastest goat?
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A leopard, whose speed is 13 m/s, chases three goats. Speeds of the goats are three integers in A.P. The goats are all initially at a distance of 100 metres from the leopard. The leopard catches the fastest goat in 20 seconds. The difference in the time taken by the leopard to catch the first two goats is (75/22) seconds. How long (in seconds) will the leopard take to catch the second fastest goat? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A leopard, whose speed is 13 m/s, chases three goats. Speeds of the goats are three integers in A.P. The goats are all initially at a distance of 100 metres from the leopard. The leopard catches the fastest goat in 20 seconds. The difference in the time taken by the leopard to catch the first two goats is (75/22) seconds. How long (in seconds) will the leopard take to catch the second fastest goat? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A leopard, whose speed is 13 m/s, chases three goats. Speeds of the goats are three integers in A.P. The goats are all initially at a distance of 100 metres from the leopard. The leopard catches the fastest goat in 20 seconds. The difference in the time taken by the leopard to catch the first two goats is (75/22) seconds. How long (in seconds) will the leopard take to catch the second fastest goat?.
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