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TIME AND DISTANCE -> IMPORTANT FACTS AND FORMULAE

1. Speed = [Distance/Time],Time=[Distance/Speed],Distance = (Speed*Time) x km/hr = [x*5/18] m/sec. If the ratio of the speeds of A and B is a:b, then the ratio of the times taken by them to cover the same distance is 1/a : 1/b or b:a. x m/sec = [x*18/5] km/hr. Suppose a man covers a certain distance at x km/hr and an equal distance at y km/hr. then, the average speed during the whole journey is [2xy/x+y] km/hr.

TIME AND DISTANCE -> EXAMPLES

1. How many minutes does John take to cover a distance of 400 m, if he runs at a speed of 20 km/hr? Sol. John’s speed = 20 km/hr = [20*5/18] m/sec = 50/9 m/sec. While covering a distance of 24 km, a man noticed that after walking for 1 hour and 40 minute, the distance covered by him was 5/7 of the remaining distance. What was his speed in metres per second? Sol. Let the speed be x km/hr. Then, distance covered in 1 hr: 40 min. i.e., 1 2/3 hrs = 5x/3 km. Remaining distance = [24-5x/3] km. ∴ 5x/3 = 5/7[24-5x/3] ⇔ 5x/3 = 5/7[72-5x/3] ⇔ 7x = 72-5x ⇔ 12x = 72 ⇔ x = 6 Hence, speed = 6 km/hr = [6*5/18] m/sec = 5/3m/sec = 1 2/3 m/sec If a man walks at athe rate of 5 kmph, he misses a train by 7 minutes. However, if he walks at the rate of 6 kmph, he reaches the station 5 minutes before the arrival of the train. Find the distance covered by him to reach the station. Sol. Let the required distance be x km. Difference in the times taken at two speeds = 12 min = 1/5 hr. ∴ x/5 - x/6 = 1/5 ⇔ 6x - 5x = 6 ⇔ x = 6. Hence, the required distance is 6 km.

TIME AND DISTANCE -> EXERCISE

1. A man takes 5 hours 45 min. In walking to a certain place and riding back. He would have gained 2 hours by riding both ways. The time he would take to walk both ways is :

• A. 11 hrs 45 min
• B. 3 hrs 45 min
• C. 7 hrs 30 min
• D. 7 hrs 45 min
 Ans: A. Sol. Let the distance be x km. Then, (time taken to walk x km) + (Time taken to ride x km) = 23/4 hrs. ⇔ (Time taken to walk 2x km) + (Tie taken to ride 2x km) = 23/2 hrs. But, time taken to ride 2x km = 15/4 hrs. ∴ Time taken to walk 2x km [23/2 - 15/4] hrs = 31/4 hrs = 7 hrs 45 min.

2. Two trains start from P and Q respectively and travel towards each other at a speed of 50 km/hr and 40 km/hr respectively. By the time they meet, the first train has travelled 100 km more than the second. The distance between P and Q is :

• A. 500 km
• B. 630 km
• C. 900 km
• D. 660 km
 Ans: C. Sol. At the time of meeting, let the distane travelled byb the second train be x km. Then, distance covered by the first train is (x + 100) km ∴ x/40 = (x+100)/50 ⇔ 50x = 40x 4000 ⇔ x = 400. So, distance between P and Q = (x+x+100) km = 900 km.

3. Two trains starting at the same time from two stations 200 km apart and going in opposite directions cross each other at a distance of 110 km from one of the stations. What is the ratio of their speeds ?

• A. 11:9
• B. 11:20
• C. 9:20
• D. 11:8
 Ans: A. Sol. In the same time, they cover 110 km and 90 km respectively. ∴ Ratio of their speeds = 110 : 90 = 11 : 9.