Two trains, one departing from Howrah to Patna and the other from Patna to Howrah, commence their journeys simultaneously. Following their encounter, the train from Howrah reaches its destination in 9 hours, while the train from Patna takes 16 hours to reach its destination. What is the ratio of their speeds?
Question
Two trains, one departing from Howrah to Patna and the other from Patna to Howrah, commence their journeys simultaneously. Following their encounter, the train from Howrah reaches its destination in 9 hours, while the train from Patna takes 16 hours to reach its destination. What is the ratio of their speeds?
Solution
The problem can be solved using the concept of relative speed.
Step 1: Understand the problem The problem states that two trains start at the same time from two different locations and meet at some point. After the meeting point, one train takes 9 hours to reach its destination and the other takes 16 hours to reach its destination. We need to find the ratio of their speeds.
Step 2: Apply the concept of relative speed In problems involving two moving objects, the concept of relative speed is often used. The relative speed of two objects moving in opposite directions is the sum of their speeds.
Step 3: Use the given information The time taken by the trains to reach their destinations after meeting each other is inversely proportional to their speeds. This is because speed = distance/time, so time = distance/speed. If the distance is the same (which it is, because they meet at the same point and then travel to their destinations), then a greater speed will mean less time, and a lesser speed will mean more time.
Step 4: Calculate the ratio The train from Howrah takes 9 hours to reach its destination after the meeting point, and the train from Patna takes 16 hours. So, the ratio of their speeds is the inverse of this, i.e., 16:9.
So, the ratio of the speed of the train from Howrah to the speed of the train from Patna is 16:9.
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