To find the ratio of time taken by the trains to travel the same distance, we need to understand the relationship between speed, distance, and time. The formula connecting these quantities is:
\(\text{Time} = \frac{\text{Distance}}{\text{Speed}}\)
Given that the speeds of the trains are in the ratio of 2 : 3 : 5, let's denote their speeds as 2x, 3x, and 5x respectively.
Since all three trains travel the same distance, let this distance be \(d\). The time taken by each train can be expressed as:
- Time taken by the first train: \(\frac{d}{2x}\)
- Time taken by the second train: \(\frac{d}{3x}\)
- Time taken by the third train: \(\frac{d}{5x}\)
The ratio of the time taken by the trains is therefore:
\(\frac{d}{2x} : \frac{d}{3x} : \frac{d}{5x}\)
Since \(d\)and \(x\)are common in all terms, they can be canceled out:
\(\frac{1}{2} : \frac{1}{3} : \frac{1}{5}\)
Thus, the correct answer is \(\frac{1}{2} : \frac{1}{3} : \frac{1}{5}\).
In conclusion, the relationship between speed and time is inversely proportional when distance is constant, which results in this given ratio of time based on the speed ratio.
Similar Questions
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Important Questions from Speed Time and Distance
A train travelling at a speed of 72 km/hr crosses a post in 20 seconds. If it crosses another train travelling at a speed of 54 km/hr in the same direction in 1 minute 45 seconds, then the difference in length between the two trains is
Rajiv's boat can travel along the current at the 8 km/hour and against the current at the rate 6 km/hour. Find the time taken by the boat to sail 28 km in still water.
Rohit and Dinesh are 64 km apart. Rohit can walk at a speed of 15 km/hr and Dinesh at the speed of 17 km/hr. In how many hours will they meet if they are travelling towards each other?
Two trains running in opposite directions cross a man standing on the platform in 25 seconds and 32 seconds respectively and they cross each other in 30 seconds. The ratio of their speed is:
A worker covers a distance of 81 km in 11 hours. He travels partly on foot at 4.5 km/h and partly on bicycle at 15 km/h. What is the distance covered on the cycle?
