A train running at the speed of 80 km/h crosses a 350 m long tunnel in 36 seconds. What is the length of the train (in meters)?
- 350
- 380
- 420
- 450
The Correct Option is D
Approach Solution - 1
The problem involves calculating the length of the train given the speed, time, and length of a tunnel. Let's solve this step by step.
First, convert the speed from km/h to m/s:
\(8060×1000 = 800003600 = 22.22\) m/s
Next, calculate the total distance covered by the train in 36 seconds:
\(22.22×36 = 800\) m
This total distance includes both the length of the train and the length of the tunnel. We know the tunnel's length is 350 m.
Therefore, the length of the train is:
\(800-350 = 450\) m
This confirms the correct answer is 450 meters.
Approach Solution -2
Let the length of the train be \(L\) meters.
The train is running at 80 km/h, which is \(80 \times \frac{1000}{3600} = \frac{800}{36} = \frac{200}{9}\) m/s.
The train crosses a 350 m long tunnel in 36 seconds.
The total distance the train covers is the length of the train plus the length of the tunnel: \(L + 350\) meters.
Distance = Speed × Time, so \(L + 350 = \frac{200}{9} \times 36 = 200 \times 4 = 800\).
\(L = 800 - 350 = 450\) meters.
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