Final answer:
The length of the train is 750 meters. The speed of the train is converted from km/hr to m/s, and then the distance the train covers in one minute is calculated. Since the train and the platform are of equal length, the calculated distance is halved to find the length of the train.
Step-by-step explanation:
To calculate the length of the train, given that it crosses a platform of equal length in one minute at a speed of 90 km/hr, we first need to convert the speed from kilometers per hour to meters per second to find out how far the train travels in one minute.
Conversion: 1 km/hr is equal to ≈ ⅟ m/s. Therefore, 90 km/hr is equal to 90 × ⅟ = 25 m/s.
Next, since the train takes one minute (or 60 seconds) to cross the platform, we calculate the distance covered, which is the combined length of the train and the platform, as follows:
Distance covered: Speed × Time = 25 m/s × 60 s = 1500 meters.
The total distance covered is the length of the train plus the length of the platform. Since these are equal, we can say that:
Length of Train + Length of Platform = 2 × Length of Train = 1500 meters.
Therefore, the length of the train is 1500 meters ÷ 2, which equals 750 meters.