A train leaves a station at 70 km/h. Another train leaves the same station 30 mi

A train leaves a station at 70 km/h. Another train leaves the same station 30 minutes later at 90 km/h. How far from the station will they meet?

A train leaves a station at 70 km/h. Another train leaves the same station 30 minutes later at 90 km/h. How far from the station will they meet?

Step 1: Understand that the first train leaves the station at a speed of 70 km/h.
Step 2: Know that the second train leaves the same station 30 minutes later at a speed of 90 km/h.
Step 3: Convert 30 minutes into hours because the speeds are in km/h. 30 minutes is 0.5 hours.
Step 4: Let 'd' be the distance from the station where the two trains meet.
Step 5: Calculate the time taken by the first train to travel distance 'd'. It is d/70 hours.
Step 6: Calculate the time taken by the second train to travel distance 'd'. It is d/90 hours.
Step 7: Since the second train leaves 0.5 hours later, the time for the second train is d/90 + 0.5.
Step 8: Set up the equation: d/70 = d/90 + 0.5.
Step 9: Solve the equation for 'd'. First, find a common denominator for the fractions, which is 630.
Step 10: Rewrite the equation: (9d)/630 = (7d)/630 + 0.5.
Step 11: Multiply everything by 630 to eliminate the denominator: 9d = 7d + 315.
Step 12: Subtract 7d from both sides: 2d = 315.
Step 13: Divide both sides by 2 to find 'd': d = 157.5 km.
Step 14: Check the calculations to ensure they are correct.

Relative Speed and Time – Understanding how to calculate the distance based on the speed of two objects moving towards each other and the time difference in their departures.
Algebraic Manipulation – Ability to set up and solve equations involving distances, speeds, and time.