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Consider two trains, both 500 meters long, on a collision course at speeds of 45 km/hr and 30 km/hr. How long will it take for the slower train to catch up and pass the driver of the faster one?
Two goods train each 500 m long, are running in opposite direction on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one.
To solve this problem, we need to follow these steps:
-
Convert speeds to meters per second:
- 45 km/hr = 45 * (5/18) m/s = 12.5 m/s
- 30 km/hr = 30 * (5/18) m/s = 8.33 m/s
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Calculate the relative speed:
- Since the trains are moving in opposite directions, their relative speed is the sum of their individual speeds.
- Relative speed = 12.5 m/s + 8.33 m/s = 20.83 m/s
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Determine the total distance traveled:
- The distance traveled is equal to the length of the slower train, as it needs to completely pass the faster train (including its driver).
- Distance = 500 m
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Calculate the time taken:
- Time = Distance / Speed
- Time = 500 m / 20.83 m/s ≈ 24 seconds
Therefore, the time taken by the slower train to pass the driver of the faster one is approximately 24 seconds.
Rate, Speed, and Distance
Rate, speed, and distance are fundamental concepts in motion and are interrelated through a simple yet powerful equation:
Distance = Rate × Time
This equation can be rearranged to solve for any of the three variables:
- Speed = Distance / Time
- Time = Distance / Rate
Here’s a breakdown of each term:
- Rate: A general term for any quantity per unit of time, not just speed. It can be used for various quantities like work rate, flow rate, etc.
- Speed: A specific type of rate, referring to distance traveled per unit of time. For example, miles per hour, kilometers per second, etc.
- Distance: The total length or displacement covered during travel.
Understanding these relationships is crucial in various real-life scenarios, such as:
- Calculating travel time: Knowing the distance and speed, you can find how long it will take to reach your destination.
- Estimating fuel consumption: Vehicles usually have fuel efficiency ratings based on miles per gallon or kilometers per liter. Knowing the distance and fuel efficiency helps estimate the required fuel.
- Planning work schedules: When tasks have predetermined rates (e.g., painting walls at a specific rate per square meter), understanding how long it will take to complete the job becomes easy with distance and rate information.
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