Vishnu travelled equal distance at speeds of 10 km/hr, 30 km/hr, and 8 km/hr, and took a total of 15.5 minutes to complete. Find the total distance he travelled, in km.a)1b)3c)4d)2Correct answer is option 'B'. Can you explain this answer?

Question

Answer

Understanding the Problem
Vishnu traveled equal distances at three different speeds: 10 km/hr, 30 km/hr, and 8 km/hr. The total time taken for the journey was 15.5 minutes. We need to find the total distance he traveled.
Convert Time to Hours
- Total time = 15.5 minutes = 15.5/60 hours = 0.2583 hours (approximately).
Let the Distance be 'd'
- He travels the same distance 'd' at each speed.
Calculate Time for Each Segment
- Time taken at 10 km/hr = d / 10 hours
- Time taken at 30 km/hr = d / 30 hours
- Time taken at 8 km/hr = d / 8 hours
Set Up the Equation
- Total time = Time at 10 km/hr + Time at 30 km/hr + Time at 8 km/hr
- Thus, we can write:
d/10 + d/30 + d/8 = 0.2583
Finding a Common Denominator
- The least common multiple (LCM) of 10, 30, and 8 is 120.
- Rewriting each term:
- d/10 = 12d/120
- d/30 = 4d/120
- d/8 = 15d/120
- Therefore:
12d/120 + 4d/120 + 15d/120 = 0.2583
Simplifying the Equation
- Combine the fractions:
(12d + 4d + 15d) / 120 = 0.2583
- This simplifies to:
31d / 120 = 0.2583
Solving for 'd'
- Multiply both sides by 120:
31d = 0.2583 * 120
- Calculate:
31d = 31 (approximately)
- Thus, d = 1 km.
Total Distance Traveled
- Since he traveled the distance 'd' three times, the total distance is:
Total Distance = 3 * 1 km = 3 km.
Thus, the correct answer is option 'B' - 3 km.

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