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 that is 1000 meters long, moving at a speed of 90 km/hr, to completely pass a 500 meter long bridge. To solve this, we will first calculate the total distance the train needs to cover (train length + bridge length) and then use the given speed to find the time taken.
Answer
The time taken for the train to pass through the bridge is $60$ seconds.
Answer for screen readers
The time taken for the train to pass through the bridge is $60$ seconds.
Steps to Solve
- Calculate Total Distance
To find the total distance the train needs to cover, add the length of the train to the length of the bridge:
$$ \text{Total Distance} = \text{Length of Train} + \text{Length of Bridge} $$
$$ \text{Total Distance} = 1000, \text{m} + 500, \text{m} = 1500, \text{m} $$
- Convert Speed to Meters per Second
The speed of the train is given in kilometers per hour. We need to convert it to meters per second using the conversion factor:
$$ 1, \text{km/hr} = \frac{5}{18}, \text{m/s} $$
Thus,
$$ \text{Speed} = 90, \text{km/hr} \times \frac{5}{18} = 25, \text{m/s} $$
- Calculate Time Taken
To find the time it takes for the train to pass the bridge, use the formula:
$$ \text{Time} = \frac{\text{Total Distance}}{\text{Speed}} $$
Thus,
$$ \text{Time} = \frac{1500, \text{m}}{25, \text{m/s}} = 60, \text{s} $$
The time taken for the train to pass through the bridge is $60$ seconds.
More Information
This calculation shows how to convert speed from kilometers per hour to meters per second, as well as how to apply the formula for time using distance and speed.
Tips
- A common mistake is not converting speed to the correct units (m/s) before using it in calculations. Always ensure unit consistency.
- Miscalculating the total distance by forgetting to include both lengths (train + bridge).
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