Two trains are coming from opposite directions with speeds of 75 km/hr and 100 km/hr on two parallel tracks. At some moment the distance between them is 100 km. After T hours, distance between them is again 100 km. T is equal to
Question
Two trains are coming from opposite directions with speeds of 75 km/hr and 100 km/hr on two parallel tracks. At some moment the distance between them is 100 km. After T hours, distance between them is again 100 km. T is equal to
Solution
The problem can be solved by using the concept of relative speed.
Step 1: Convert the speeds from km/hr to km/min by dividing by 60. So, the speeds become 75/60 km/min and 100/60 km/min.
Step 2: When two objects are moving in opposite directions, their relative speed is the sum of their individual speeds. So, the relative speed of the two trains is (75/60 + 100/60) km/min = 175/60 km/min.
Step 3: The trains are initially 100 km apart. They will be 100 km apart again when they have travelled a combined distance of 200 km (100 km to meet in the middle, and 100 km to be 100 km apart again).
Step 4: The time it takes for the trains to travel this distance is the total distance divided by their relative speed. So, T = 200 km / (175/60 km/min) = 200 * 60 / 175 min.
Step 5: Convert the time from minutes to hours by dividing by 60. So, T = 200 * 60 / 175 / 60 hr = 400/7 hr.
So, T is approximately 57.14 hours.
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