Two trains 135 meters and 105 meters in length, are running towards each other on parallel lines, one at the rate of 41 km/hr and the other at 31 km/ hr. How much time (in seconds) will they take to pass each other from the moment they meet?Answer( Please choose a correct answer ) CLEAR8 seconds10 seconds15 seconds12 seconds
Question
Two trains 135 meters and 105 meters in length, are running towards each other on parallel lines, one at the rate of 41 km/hr and the other at 31 km/ hr. How much time (in seconds) will they take to pass each other from the moment they meet?Answer( Please choose a correct answer ) CLEAR8 seconds10 seconds15 seconds12 seconds
Solution
To solve this problem, we first need to understand that when two objects are moving towards each other, their relative speed is the sum of their individual speeds.
Step 1: Convert the speeds from km/hr to m/s We know that 1 km/hr = 5/18 m/s. So, 41 km/hr = 41 * (5/18) = 11.39 m/s (approximately) 31 km/hr = 31 * (5/18) = 8.61 m/s (approximately)
Step 2: Calculate the relative speed The trains are moving towards each other, so their relative speed is the sum of their individual speeds = 11.39 m/s + 8.61 m/s = 20 m/s.
Step 3: Calculate the total distance to be covered The trains will have passed each other completely when they have covered a distance equal to the sum of their lengths = 135 m + 105 m = 240 m.
Step 4: Calculate the time taken to cover this distance We know that time = distance/speed. So, the time taken for the trains to pass each other = total distance / relative speed = 240 m / 20 m/s = 12 seconds.
So, the correct answer is 12 seconds.
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