Time, speed and distance
- A train running at 90 km/h passes a man walking at 6 km/h in the same direction in 12 seconds. What is the length of the train? Answer: A. 280 m Answer: (A) 280 m Relative speed = 90 − 6 = 84 km/h = 70/3 m/s. Length = 70/3 × 12 = 280 m. 1
- In a 1 km race, A beats B by 40 m or by 8 seconds. How long does A take to run the race? Answer: C. 192 seconds Answer: (C) 192 seconds B runs the last 40 m in 8 s, so B's speed = 5 m/s and B's time = 1000 ÷ 5 = 200 s. A finishes... 1
- Two runners start together from the same point on a 600 m circular track and run in the same direction at 4 m/s and 6 m/s. After how long will they first meet again? Answer: B. 300 seconds Answer: (B) 300 seconds The faster runner must gain one full lap (600 m) at a relative speed of 2 m/s. Time = 600 ÷ 2... 1
- A train is running 20 minutes late. By increasing its speed by 16 km/h it covers the next 160 km and arrives on time. What is its usual speed? Answer: A. 80 km/h Answer: (A) 80 km/h 160/v - 160/v + 16 = 1/3 , so v(v + 16) = 160 × 16 × 3 = 7680. 80 × 96 = 7680, so v = 80 km/h. (Check... 1
- Stations A and B are 190 km apart. A train leaves A at 6 a.m. towards B at 30 km/h. Another train leaves B at 7 a.m. towards A at 50 km/h. At what time do they meet? Answer: C. 9 a.m. Answer: (C) 9 a.m. By 7 a.m. the first train has covered 30 km, leaving a gap of 160 km. From 7 a.m. they close the gap at... 1
- A train passes two men walking in the same direction as the train at 3 km/h and 5 km/h in 10 seconds and 11 seconds respectively. What is the speed of the train? Answer: A. 25 km/h Answer: (A) 25 km/h The train's length is the same both times: (v − 3) × 10 = (v − 5) × 11 (the 5/18 factor cancels). 10v... 1
- Without stoppages a bus runs at 64 km/h; including stoppages its average speed is 48 km/h. For how many minutes per hour does the bus stop? Answer: D. 15 minutes Answer: (D) 15 minutes In one hour the bus loses 64 − 48 = 16 km of running. At 64 km/h that takes 16/64 × 60 = 15 min... 1
- Two trains start at the same time from P and Q towards each other. After meeting, they take 4 hours and 9 hours respectively to reach their destinations. If the train from P runs at 60 km/h, what is the speed of the train from Q? Answer: A. 40 km/h Answer: (A) 40 km/h Shortcut: S_P/S_Q = √(t_Q/t_P) = √(9/4) = 3/2 . S_Q = 60 × 2/3 = 40 km/h. Trap: 90 km/h inverts the r... 1
- A train 240 m long crosses a pole in 12 seconds. How long will it take to cross a platform 360 m long? Answer: D. 30 s Answer: (D) 30 s Speed = 240/12 = 20 m/s. To cross the platform the train covers 240 + 360 = 600 m. Time = 600/20 = 30 s. 1