Two trains are moving in opposite directions at 80 km/h and 64 km/h. Their lengths are 2.1 km and 1.9 km respectively. What is the time taken by the slower train to cross the faster train (in seconds)?
Question
Two trains are moving in opposite directions at 80 km/h and 64 km/h. Their lengths are 2.1 km and 1.9 km respectively. What is the time taken by the slower train to cross the faster train (in seconds)?
Solution
Sure, here's how you can solve this problem:
Step 1: First, we need to find the relative speed of the two trains. Since they are moving in opposite directions, we add their speeds. So, the relative speed is 80 km/h + 64 km/h = 144 km/h.
Step 2: We need to convert this speed into m/s because the lengths of the trains are given in km and we want the time in seconds. We know that 1 km/h = 5/18 m/s. So, 144 km/h = 144 * (5/18) = 40 m/s.
Step 3: Now, we find the total length of the two trains which is 2.1 km + 1.9 km = 4 km = 4000 m (since 1 km = 1000 m).
Step 4: Finally, we find the time taken by the slower train to cross the faster train. We know that time = distance/speed. So, the time taken is 4000 m / 40 m/s = 100 seconds.
So, the slower train takes 100 seconds to cross the faster train.
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