To find the length of the second train, we can use the concept of relative speed and the formula for relative motion. Given two trains moving in the same direction, their relative speed is the difference in their speeds.
- First, convert the speeds from km/h to m/s, because the length of the trains are given in meters and the time in seconds.
- The first train's speed: 40 \ \text{km/h} = 40 \times \frac{1000}{3600} \ \text{m/s} = \frac{100}{9} \ \text{m/s}.
- The second train's speed: 22 \ \text{km/h} = 22 \times \frac{1000}{3600} \ \text{m/s} = \frac{55}{9} \ \text{m/s}.
- Calculate the relative speed:
- The relative speed when both are moving in the same direction is: \left(\frac{100}{9} - \frac{55}{9}\right) \ \text{m/s} = \frac{45}{9} \ \text{m/s} = 5 \ \text{m/s}.
- According to the problem, the trains take 1 minute to cross each other completely, which is 60 seconds.
- The total distance covered relatively in these 60 seconds at 5 m/s is:
- \text{Distance} = \text{Relative speed} \times \text{Time} = 5 \times 60 = 300 \ \text{meters}.
- The total length of both trains combined is 300 meters according to the distance calculation.
- Given the length of the first train is 125 meters, the length of the second train can be calculated as:
- \text{Length of second train} = 300 - 125 = 175 \ \text{meters}.
Thus, the length of the second train is 175 meters.
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Important Questions from Speed Time and Distance
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