Answer:
4:00 PM
Step-by-step explanation:
To determine when the second train will catch up with the first train, we need to calculate the time it takes for the second train to cover the distance that the first train has already traveled.
Begin by calculating the head start of the first train. Since the first train leaves two hours before the second train and travels at a speed of 60 km/h, the distance covered by the first train in those first two hours is:
[tex]\text{Head start distance}=60 \text{ km/h} \times 2 \text{ hours} = 120 \text{ km}[/tex]
Next, determine the relative speed between the two trains. Since both trains are traveling in the same direction, the relative speed is the difference in their speeds:
[tex]\text{Relative Speed}=80 \text{ km/h} - 60 \text{ km/h} = 20 \text{ km/h}[/tex]
To find out how long it takes for the second train to catch up with the first train, divide the head start distance by the relative speed:
[tex]\text{Time to catch up}=\dfrac{120 \text{ km}}{20 \text{ km/h}} = 6 \text{ hours}[/tex]
Since the second train leaves at 10:00 AM and takes 6 hours to catch up with the first train, the second train will catch up with the first train at:
[tex]10:00\text{ AM}+6\text{ hours}=4:00\text{ PM}[/tex]
Therefore, the second train will catch up with the first train at 4:00 PM.
