Train Speed and Length Calculation
This problem requires finding the length of Train B. We are given the speeds of two trains (A and B) moving in opposite directions, the length of Train A, and the time they take to cross each other.
Relative Speed Concept
When two objects move towards each other (opposite directions), their relative speed is the sum of their individual speeds. This is the effective speed at which they cover the distance between them.
- Speed of Train A (\(S_A\)) = 66 km/hr
- Speed of Train B (\(S_B\)) = 60 km/hr
- Length of Train A (\(L_A\)) = 240 m
- Time to cross (\(T\)) = 10 seconds
Speed Conversion
To use the formula Distance = Speed × Time, units must be consistent. Convert speeds from km/hr to m/s.
The conversion factor is: 1 km/hr = \(\frac{5}{18}\) m/s.
- \(S_A = 66 \times \frac{5}{18} = \frac{11 \times 5}{3} = \frac{55}{3}\) m/s
- \(S_B = 60 \times \frac{5}{18} = \frac{10 \times 5}{3} = \frac{50}{3}\) m/s
Calculate Relative Speed
Since trains A and B are moving in opposite directions, their relative speed (\(S_{rel}\)) is:
\(S_{rel} = S_A + S_B\)
\(S_{rel} = \frac{55}{3} + \frac{50}{3} = \frac{105}{3} = 35 \text{ m/s}\)
Calculate Total Distance
The total distance (\(D\)) covered when two trains cross each other is the sum of their lengths (\(L_A + L_B\)). This distance equals relative speed multiplied by time.
\(D = S_{rel} \times T\)
\(D = 35 \text{ m/s} \times 10 \text{ s} = 350 \text{ m}\)
Determine Length of Train B
We know that the total distance is the sum of the lengths of the two trains:
\(D = L_A + L_B\)
Substitute the known values:
\(350 \text{ m} = 240 \text{ m} + L_B\)
Solve for \(L_B\):
\(L_B = 350 \text{ m} - 240 \text{ m}\)
\(L_B = 110 \text{ m}\)
The length of Train B is 110 meters.
Similar Questions
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Important Questions from Problem on Trains
Eight railway stations A, B, C, D, E, F, G and H are connected either by two-way passages or one-way passages. One-way passages are from C to A, E to G, B to F, D to H, G to C, E to C and H to G. Two-way passages are between A and E, G and B, F and D, and E and D.
If the route between G and C is closed, which one of the following stations need not be passed through while travelling from H to C?
A daily train is to be introduced between station A and station B starting from each end at 6 AM and the journey is to be completed in 42 hours. What is the number of trains needed in order to maintain the Shuttle Service?
A train with a uniform speed passes a 122 meters long platform in 17 seconds and a 210 meters long bridge in 25 seconds. The speed of the train is:
How long does a train 153 meters long running at the rate of 90 kmph take to cross a bridge 622 meters in length?
A train passes a 360 metre long platform in 40 seconds and a man standing on the platform in 16 seconds. The speed of the train is:
