Train A leaves Chittagong at 6 AM and reaches Dhaka at 4 PM. Train B leaves Dhaka at 7 AM and reaches Chittagong at 7:30 PM. At what time do the two trains cross one another?
Question
Train A leaves Chittagong at 6 AM and reaches Dhaka at 4 PM. Train B leaves Dhaka at 7 AM and reaches Chittagong at 7:30 PM. At what time do the two trains cross one another?
Solution
To solve this problem, we need to calculate the time at which both trains meet.
Step 1: Calculate the total travel time for each train. Train A travels from 6 AM to 4 PM, which is 10 hours. Train B travels from 7 AM to 7:30 PM, which is 12.5 hours.
Step 2: Determine the time at which both trains start traveling towards each other. Train A starts at 6 AM and Train B starts at 7 AM. So, they start traveling towards each other at 7 AM.
Step 3: Calculate the total time they travel towards each other. From 7 AM to 4 PM (when Train A reaches Dhaka), it's 9 hours.
Step 4: Calculate the ratio of their speeds. The speeds of the trains are in the ratio of their travel times, which are 10 (for Train A) and 12.5 (for Train B). So, the speed ratio is 10/12.5 = 0.8.
Step 5: Calculate the time at which they meet. They meet at a time that splits the 9 hours in the ratio of their speeds. This time is 9 hours * (0.8 / (1 + 0.8)) = 4.5 hours.
Step 6: Determine the actual time of the day they meet. They start at 7 AM and meet after 4.5 hours. So, they meet at 7 AM + 4.5 hours = 11:30 AM.
So, the two trains cross each other at 11:30 AM.
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