Train A, with a length of 120 metres, is moving at a speed of 108 km/hr. Simultaneously, on a parallel track, Train B, which is 180 metres long, travels 72 km/hr in the same direction as Train A. How many seconds will it take for Train A to completely overtake Train B, if currently, Train A is just behind Train B?
Question
Train A, with a length of 120 metres, is moving at a speed of 108 km/hr. Simultaneously, on a parallel track, Train B, which is 180 metres long, travels 72 km/hr in the same direction as Train A. How many seconds will it take for Train A to completely overtake Train B, if currently, Train A is just behind Train B?
Solution 1
First, we need to convert the speeds from km/hr to m/s because the lengths of the trains are given in meters and we need to find the time in seconds.
1 km/hr = 5/18 m/s
So, the speed of Train A = 108 km/hr = 108 * 5/18 = 30 m/s And the speed of Train B = 72 km/hr = 72 * 5/18 = 20 m/s
Since the trains are moving in the same direction, we subtract the speed of Train B from the speed of Train A to get the relative speed.
Relative speed = Speed of Train A - Speed of Train B = 30 m/s - 20 m/s = 10 m/s
Next, we need to find the total distance that Train A needs to cover to completely overtake Train B. This is the sum of the lengths of Train A and Train B.
Total distance = Length of Train A + Length of Train B = 120 m + 180 m = 300 m
Finally, we find the time it takes for Train A to overtake Train B by dividing the total distance by the relative speed.
Time = Total distance / Relative speed = 300 m / 10 m/s = 30 seconds
So, it will take 30 seconds for Train A to completely overtake Train B.
Solution 2
Step 1: Convert the speeds from km/hr to m/s
Speed of Train A = 108 km/hr = 108 * (1000/3600) m/s = 30 m/s Speed of Train B = 72 km/hr = 72 * (1000/3600) m/s = 20 m/s
Step 2: Calculate the relative speed
Since the trains are moving in the same direction, the relative speed will be the difference of the two speeds.
Relative speed = Speed of Train A - Speed of Train B = 30 m/s - 20 m/s = 10 m/s
Step 3: Calculate the total distance to be covered
The total distance to be covered for Train A to completely overtake Train B is the sum of the lengths of Train A and Train B.
Total distance = Length of Train A + Length of Train B = 120 m + 180 m = 300 m
Step 4: Calculate the time taken to cover the total distance
The time taken to cover a certain distance is given by the formula:
Time = Distance / Speed
Therefore, the time taken for Train A to overtake Train B is:
Time = Total distance / Relative speed = 300 m / 10 m/s = 30 seconds
So, it will take 30 seconds for Train A to completely overtake Train B.
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