How long does a train 1000 m long moving at a speed of 90 km/hr take to pass through a 500 m long bridge?
Understand the Problem
The question is asking for the time it takes for a train with a length of 1000 m, moving at a speed of 90 km/hr, to completely pass through a bridge that is 500 m long. This requires calculations involving distance, speed, and time.
Answer
The time required is $60 \, \text{seconds}$.
Answer for screen readers
The time required for the train to completely pass through the bridge is $60 , \text{seconds}$.
Steps to Solve
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Calculate Total Distance To find the total distance the train must cover to pass the bridge completely, add the length of the train to the length of the bridge: $$ \text{Total Distance} = \text{Length of Train} + \text{Length of Bridge} = 1000 , \text{m} + 500 , \text{m} = 1500 , \text{m} $$
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Convert Speed from km/hr to m/sec To use consistent units, convert the speed of the train from kilometers per hour to meters per second: $$ \text{Speed} = 90 , \text{km/hr} \times \frac{5}{18} = 25 , \text{m/sec} $$
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Calculate Time Taken to Pass the Bridge Now, use the formula for time, where time is equal to distance divided by speed: $$ \text{Time} = \frac{\text{Total Distance}}{\text{Speed}} = \frac{1500 , \text{m}}{25 , \text{m/sec}} = 60 , \text{sec} $$
The time required for the train to completely pass through the bridge is $60 , \text{seconds}$.
More Information
The calculation shows that it takes 1 minute for the train to completely clear the 500 m bridge. This example is useful for understanding how to work with distance, speed, and time in practical scenarios.
Tips
- Failing to add the lengths of the train and bridge correctly, which leads to an incorrect total distance.
- Confusing units when converting speeds (e.g., forgetting to use the conversion factor correctly).
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