A train takes 18 seconds to pass completely through a station 162 m long and 15 seconds through another station 120 m long, at the same speed. What is the length of the train, in meters?
Step-by-step Solution:
1. Find the Difference in Distance and Time
- The key insight is that the extra time the train takes for the longer station is used to cover the extra distance.
- Difference in Station Lengths = 162 m - 120 m = 42 m.
- Difference in Time Taken = 18 s - 15 s = 3 s.
2. Calculate the Train's Speed
- The train covers the extra 42 meters in 3 seconds. We can find its speed from this.
- Speed = Distance ÷ Time = 42 m ÷ 3 s = 14 m/s.
3. Find the Length of the Train (L)
- Now we can use the speed with either of the original scenarios. Let's use the second one (120 m station in 15 s).
- When a train crosses a station, the total distance it covers is its own length plus the station's length (L + 120).
- Using the formula Distance = Speed × Time:
- L + 120 = 14 m/s × 15 s
- L + 120 = 210
- L = 210 - 120 = 90 meters.
Final Answer: The length of the train is 90 meters.