A train leaves a station and travels at 90 km/h. Another train leaves the same station 30 minutes later and travels at 120 km/h. How far from the station will they meet?
Practice Questions
1 question
Q1
A train leaves a station and travels at 90 km/h. Another train leaves the same station 30 minutes later and travels at 120 km/h. How far from the station will they meet?
90 km
120 km
150 km
180 km
Let the distance be d. Time taken by first train = d/90. Time taken by second train = d/120. Setting up the equation gives d = 150 km.
Questions & Step-by-step Solutions
1 item
Q
Q: A train leaves a station and travels at 90 km/h. Another train leaves the same station 30 minutes later and travels at 120 km/h. How far from the station will they meet?
Solution: Let the distance be d. Time taken by first train = d/90. Time taken by second train = d/120. Setting up the equation gives d = 150 km.
Steps: 11
Step 1: Understand that the first train leaves the station and travels at a speed of 90 km/h.
Step 2: The second train leaves the same station 30 minutes later and travels at a speed of 120 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'. The formula is time = distance/speed, so time for the first train is d/90 hours.
Step 6: Calculate the time taken by the second train to travel the same distance 'd'. The time for the second train is d/120 hours.
Step 7: Since the second train leaves 0.5 hours later, the time taken by the second train is (d/120) + 0.5 hours.
Step 8: Set the time taken by both trains equal to each other because they meet at the same time: d/90 = (d/120) + 0.5.
Step 9: Solve the equation for 'd'. First, multiply everything by 360 (the least common multiple of 90 and 120) to eliminate the denominators: 4d = 3d + 180.
Step 10: Simplify the equation: 4d - 3d = 180, which gives d = 180 km.
Step 11: Therefore, the distance from the station where the two trains meet is 180 km.
