Which of the following statements about train-crossing problems are CORRECT?
Statements 1, 2 and 3 are correct. For opposite directions, relative speed is the sum, not the difference.
A man rows a boat upstream at 6 km/h and downstream at 14 km/h. What is the speed of the river current in km/h?
Speed of current = (Downstream speed - Upstream speed) / 2 = (14 - 6) / 2 = 4 km/h.
A and B run a 1 km race. A beats B by 100 meters or 10 seconds. Find A's speed in m/s.
B covers 100 m in 10 s, so B's speed = 10 m/s. B takes 1000 / 10 = 100 s for 1 km. A takes 100 - 10 = 90 s. A's speed = 1000 / 90 = 11.11 m/s.
Two cars start from points P and Q towards each other at 45 km/h and 55 km/h respectively. If distance PQ is 300 km, after how many hours will they meet?
Relative speed = 45 + 55 = 100 km/h. Time to meet = Distance / Relative speed = 300 / 100 = 3 hours.
Walking at 3/4 of his usual speed, a person reaches his office 15 minutes late. What is his usual time to reach office in minutes?
Ratio of usual speed to new speed = 4 : 3. Ratio of usual time to new time = 3 : 4. Difference = 1 unit = 15 min. Usual time = 3 * 15 = 45 minutes.