Rajdhani Train running at a speed of 54 km/hr crosses a platform of length same as that of the train in 36 sec. If a Duronto train, which is 230 meters long crosses the same platform in 25 sec, then find speed of Duronto train (in km/hr)?
Step-by-step Solution:
This is a two-part problem. First, we'll use the information about the Rajdhani train to find the length of the platform. Then, we'll use that length to find the speed of the Duronto train.
1. Convert Rajdhani's Speed to m/s - To work with meters and seconds, we convert the speed:
- Speed = 54 km/hr × (5/18) = 15 m/s.
2. Find the Platform Length (L) - The problem states the train's length and the platform's length are the same (L).
- The total distance the train covers to cross the platform is L (train) + L (platform) = 2L.
- Using the formula Distance = Speed × Time:
- 2L = 15 m/s × 36 s = 540 m
- L = 540 / 2 = 270 meters.
1. Find the Total Distance Covered by Duronto - The Duronto train (230 m) crosses the same platform (270 m).
- Total Distance = Length of Duronto + Length of Platform
- Total Distance = 230 m + 270 m = 500 m.
2. Calculate Duronto's Speed in m/s - It covers this distance in 25 seconds.
- Speed = Distance ÷ Time = 500 m ÷ 25 s = 20 m/s.
3. Convert Speed to km/hr - To get the final answer in km/hr, we convert back by multiplying by 18/5.
- Speed in km/hr = 20 m/s × (18/5) = 4 × 18 = 72 km/hr.
Final Answer: The speed of the Duronto train is 72 km/hr.