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The speeds of three cars are in the ratio of 3:4:8. The ratio of the time taken by these cars for travelling the same distance is:
8:6:3
6:8:3
8:3:6
6:3:8
To find the ratio of the time taken by the cars to travel the same distance, we need to understand the relationship between speed, distance, and time.
- Speed and Time Relationship: Time is inversely proportional to speed when the distance is constant. This means if one car is faster, it takes less time to cover the same distance.
- Given Speed Ratio: 3:4:8. This means if the first car's speed is 3 units, the second's is 4 units, and the third's is 8 units.
- Time Ratio Calculation:
- For the first car: Time∝1Speed=13
- For the second car: Time∝14
- For the third car: Time∝18
- Time Ratio: Inverting the speed ratio 3:4:8 gives you 1/3 : 1/4 : 1/8. To compare these, find a common factor and invert:
- Convert to whole numbers: Multiply by the least common multiple of 3, 4, and 8, which is 24.
- 13×24=8
- 14×24=6
- 18×24=3
- Final Ratio of Times: 8:6:3
- Correct Option: 8:6:3―
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