A train leaves a station at 80 km/h and another train leaves the same station 30

A train leaves a station at 80 km/h and another train leaves the same station 30 minutes later at 100 km/h. How far from the station will they meet?

A train leaves a station at 80 km/h and another train leaves the same station 30 minutes later at 100 km/h. How far from the station will they meet?

Step 1: Understand that the first train leaves the station at a speed of 80 km/h.
Step 2: Know that the second train leaves the same station 30 minutes later at a speed of 100 km/h.
Step 3: Convert 30 minutes into hours. 30 minutes is equal to 0.5 hours.
Step 4: Let 't' be the time in hours that the first train travels before they meet.
Step 5: The first train travels for 't' hours, so the distance it covers is 80t kilometers.
Step 6: The second train starts 0.5 hours later, so it travels for (t - 0.5) hours.
Step 7: The distance the second train covers is 100(t - 0.5) kilometers.
Step 8: Set the distances equal to each other because they meet at the same point: 80t = 100(t - 0.5).
Step 9: Solve the equation: 80t = 100t - 50.
Step 10: Rearrange the equation to find t: 100t - 80t = 50, which simplifies to 20t = 50.
Step 11: Divide both sides by 20 to find t: t = 50 / 20 = 2.5 hours.
Step 12: Now, calculate the distance the first train travels: Distance = speed * time = 80 * 2.5 = 200 km.
Step 13: Therefore, the distance from the station where they meet is 200 km.

Relative Speed and Time – Understanding how to calculate the distance traveled by two objects moving at different speeds and starting at different times.
Algebraic Manipulation – Using algebra to set up and solve equations based on the relationship between distance, speed, and time.