Select the correct answerTwo trains, 80 km apart, are travelling in the same direction. Train B travelling at 80 km/hr. starts at 10 AM. Train A, which was traveling at 105 km/hr, starts at 10:30 AM. Find the time at which faster train overtakes the other?radio_button_unchecked3 amradio_button_unchecked3:20 pmradio_button_unchecked3:18 pm
Question
Select the correct answerTwo trains, 80 km apart, are travelling in the same direction. Train B travelling at 80 km/hr. starts at 10 AM. Train A, which was traveling at 105 km/hr, starts at 10:30 AM. Find the time at which faster train overtakes the other?radio_button_unchecked3 amradio_button_unchecked3:20 pmradio_button_unchecked3:18 pm
Solution
Step 1: Determine the relative speed of the two trains. Since they are moving in the same direction, we subtract the speed of the slower train from the speed of the faster train. So, 105 km/hr - 80 km/hr = 25 km/hr.
Step 2: Determine the time it takes for Train A to catch up to Train B. Since Train B had a 30-minute head start, it has already traveled 40 km (half of its hourly speed) by the time Train A starts. So, the distance Train A needs to cover to catch up to Train B is 80 km (the original distance between them) + 40 km (the distance Train B traveled in the first 30 minutes) = 120 km.
Step 3: Calculate the time it takes for Train A to cover this distance at its relative speed. Time = Distance / Speed, so Time = 120 km / 25 km/hr = 4.8 hours.
Step 4: Add this time to the time Train A started to find the time it overtakes Train B. 10:30 AM + 4.8 hours = 3:18 PM.
So, the correct answer is 3:18 PM.
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