Train A leaves Station X at 5:00 AM at 50 km/h. Train B leaves Station Y at 7:30 AM at 80 km/h. Both trains move towards each other . Distance = 500 km. When do they meet?

Correct Answer: 10:23 AM

To find the exact time when Train A and Train B meet, we can break the problem down into simple steps by analyzing the time elapsed, the distance covered by each train, and their relative speeds.

Step 1: Understand the given details
• Distance between Station X and Station Y = 500 km
• Speed of Train A (leaves Station X at 5:00 AM) = 50 km/h
• Speed of Train B (leaves Station Y at 7:30 AM) = 80 km/h
• Both trains are moving towards each other.

Step 2: Calculate the distance Train A covers before Train B starts moving
Train A starts at 5:00 AM, while Train B starts at 7:30 AM.
Time difference between 5:00 AM and 7:30 AM = 2 hours 30 minutes = 2.5 hours.
Distance traveled by Train A in 2.5 hours can be calculated using the formula:

$\text{Distance}=\text{Speed}\×\text{Time}$

$\text{Distance covered by Train A}=50\×2.5=125\text{km}$

Step 3: Calculate the remaining distance between the two trains at 7:30 AM
At 7:30 AM, Train A has already traveled 125 km out of 500 km.

$\text{Remaining Distance}=500-125=375\text{km}$

Step 4: Calculate the relative speed of the two trains
Since both trains are moving towards each other, their relative speed is the sum of their individual speeds:

$\text{Relative Speed}=50+80=130\text{km/h}$

Step 5: Calculate the time taken for the trains to meet after 7:30 AM
Time required to cover the remaining 375 km at a relative speed of 130 km/h:

$\text{Time}=\frac{\text{Remaining Distance}}{\text{Relative Speed}}$

$\text{Time}=\frac{375}{130}=\frac{75}{26}$

Convert this improper fraction into hours and minutes:

$\frac{75}{26}=2\text{hours and}\frac{23}{26}\text{hours}$

Convert the fractional part to minutes:

$\frac{23}{26}\×60=\frac{1380}{26}\≈53.07\text{minutes}$

Thus, the time taken is approximately 2 hours and 53 minutes (or about 2 hours and 53 minutes rounded).

Step 6: Determine the exact meeting time
Adding 2 hours and 53 minutes to 7:30 AM gives 10:23 AM (approximated according to standard clock problem options).

Therefore, the trains will meet at 10:23 AM.