Average Speed Average Speed = (Total distance traveled)/(Total time taken)
Case 1 – When the distance is constant:
Average speed = 2xy/x+y; Where, x and y are the two speeds at which the same distance has been covered.
Case 2 – When the time taken is constant:
Average speed = (x + y)/2; Where, x and y are the two speeds at which we traveled for the same time.
Relative speed: When two bodies are moving in same direction with speeds s1and s2respectively, their relative speed is the difference of their speeds. i.e. Relative Speed=s1-s2
When two bodies are moving in opposite direction with speeds s1and s2 respectively, their relative speed is the sum of their speed. i.e. Relative Speed=s1+s2
Conversion of Units
It is extremely important to pay attention to the units for each of the quantities given. At times, you may be required to convert the unit of speed from km per hr to metre per second or vice versa.
Converting km/hr into m/s
km 1000 m 5 = = m/s hr 60 x 60 sec 18
Example: km 5 20 = 20 x = 5.55 m/sec hr 18
Converting m/s into km/hr:
m 18 = km/hr s 5
Example: m 18 20 = 20 x = 72 km/hr s 5 From conversion from km/hr to m/s, multiply it by 5/18. Conversion of m/s to km/hr, multiply by 18/5.
To convert minutes into seconds, multiply by 60
To convert hours into seconds, multiply by 60 x 60
1).
i).Express a speed of 36km/hr in m/sec
ii). 108km/hr in m/sec
iii). 144km/hr in m/sec
2).
i). Express 25m/sec in km/hr
ii). 50m/sec in km/hr
iii). 100 m/sec in km/hr
1. Find the Distance traveled by a person, if he travels at speed of 45 km/hr
for 3 hours. A)90km B)135km C)145km 15km 2. If a person covers distance of 100km at a speed 20km/hour, then time taken to complete the journey is A) 10 Hour B) 5 Hour C)15 Hour D)8 Hour 3. Find the speed of the person, if he travels 200 km in 5 hour A) 40 km/ hour B) 20 km/ hour C)20 km/ hour D)50 km/ hour 4.A missile travels at 1350 km/hr. How many metres does it travel in one second? A)369 m B) 375m C)356m D)337m 5. A person covers a distance of 12km, while walking at a speed of 4km/h . How much distance he would cover in same time, If he walks at a speed of 6km/h A)20km B)19km C)24km D) 18km 6. A car travelling at the average speed of 30km/hr covers a distance in 6 hours. Find the speed of another car which covers the same distance in 5 hour? A.24km/hr B. 25km/hr C. 36km/hr D. 42km/hr 7. A car travelling at a speed of 40km/hr can complete a journey in 9 hours. How long will it to take to travel the same distance at 60km/hr? A. 6 hr B. 3 hr C. 4 hr D. 1.5 hr 8. A car a journey at the speed of 80km/hr in 10 hours. If the same distance is to be covered in 4 hours, by how much the speed of the car will have to increase? A. 89 km/hr B. 100 km/hr C. 120 km/hr D. 160 km/hr Problems based on ratio’s 9. The ratio of speeds of A:B is 1:4. If B covers a distance in 20 min, A will cover it in 40 B .10 C. 5 D.80 10. One car completes journey of 600 km in 30 hours and the other car completes the journey of 550 kms in 11 hours. The ratio of their average speed is A.2:5 B. 3:2 C.1:4 D. 5:2 11.The ratio between the speeds of two trains is 7 : 8. If the second train runs 160 km in 4 hours, then the speed of the first train is A. 35 km/hr B. 40 km/hr C. 120 km/hr D. 160 km/hr 12.The ratio of speeds of A & B is 4 : 5. If difference between time taken by two in covering a certain distance is 20 minutes, find the time taken by A? A.44 min B. 55 min C. 80 min D. 100 min 13. Walking ( 3/4)th of his usual speed, a person is 20 min late to his office. Find his usual time to cover the distance? A.30 min B. 20 min C. 60 min D. 80 min Problems based on Average Speed 14. A man covers a certain distance by car driving at 20 km/hr and he returns back to the starting point riding on a scooter at 30 km/hr. Find his average speed for the whole journey A)25km/hr B. 24 km/hr C. 22.5km/hr D. 20km/hr 15. A man covers a certain distance by driving a car at 20km/hr and he returns back to the starting point riding on a scooter at 40km/hr. Find his average speed for the whole journey? A. 20km/hr B. 26.6km/hr C. 30km/hr D. 34km/hr 16. If a person covers 40km at a speed of 10km/hr by a cycle, 25km at 5km/hr on foot and another 100km at 50km/h by bus. Then find his average speed for the whole journey? A). 20km/hr B). 15km/hr C). 30km/hr. D). 60km/hr Based on Time 17. A boy goes to school at a speed of 3 km/hr and returns to the village at a speed of 2 km/hr. If he takes 5 hrs in all, what is the distance between the village and the school A.12km B. 3km C. 4km D. 6km 18. Two cyclist cover the same distance at 15 km/hr and 16 km/hr, respectively. Find the distance travelled by each, if one takes 16 minutes longer than other does A.32km B. 64km C. 96 km D. 85km 19. A thief is spotted by a policeman at a distance of 200m. If the speed of the thief is 10km/hr and that of the policeman is 12km/hr, how long will the policeman have to run to catch the thief? A. 1 km B. 1.2 km C. 2 km D. 2.4 km
Late/Early Problems 20. A person travels a certain distance at 3 km/hr and reaches 15 min late. If he travels at 4 km/hr, he reaches 15 min earlier. The distance he has to travel is, A. 4.5 km B. 6 km C. 7.2 km D. 12 km E. None of these 21. A man riding a bicycle from his house at 10 km/hr and reaches his office late by 6 min. He increased by 2 km/hr and reaches 6 min before. How far is the office from his house? A. 6 km/hr B. 7 km/hr C. 12 km/hr D. 16 km/hr Problems on trains
Important Points to Remember
1) If the length of one train is P and the length of second train is Q, the total distance to be covered is (P+Q)
2) Finding Relative speed:
3) If two trains of lengths P and Q move in opposite directions at V1 m/s and
V2 m/s, then time taken by the trains to cross each other, can be calculated by (P + Q) Time Taken = (V1 + V2)
4) If two trains of different lengths P and Q move in same direction at V1 m/s and V2 m/s, then time taken by the trains to cross each other, is calculated by (P + Q) Time Taken = (V1 – V2)
Quick Tips and Tricks
1) The distance traveled by train when it crosses a platform is equal to the sum of the length of the train and length of the platform Time taken by a train of length L meter to pass a signal post or standing man = Time taken by the train to cover L meter. L Time = Speed A signal post or a standing man is considered to be the point object.
2) The time taken by a train of length L 1 meter to pass a stationary object of length L2 is basically the time taken by the train to cover (L 1 + L2) meter. (L1 + L2) Time = Speed
3) The time taken by a train of length L 1 meter to pass a moving object of length L2 is determined by considering the relative speed between the moving objects. (L1 + L2) Time = Rs Rs is the relative speed between moving objects in same or opposite direction. L1 is the length of train. L2 is the length of moving object other than train.
4) Two trains start from two points P and Q at the same time and move towards each other. These trains take p and q seconds to reach points Q and P respectively, the relation between them is given by
(P's Speed) q = (Q's Speed) p 5) When two trains X and Y start moving towards each other at the same time from points A and B and after crossing each other the train X reaches point B in a seconds and train Y reaches points A in b seconds, then
Train X speed: Train Y speed = b1/2: a1/2
1. A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train? A.120 metres B.180 metres C.324 metres D.150 metres
2.A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long? A.40 sec B.42 sec C.45 sec D.48 sec 3.A goods train runs at the speed of 72 kmph and crosses a 250 m long platform in 26 seconds. What is the length of the goods train? A.230 m B.240 m C.260 m D.270 m 4.A train 240 m long passes a pole in 24 seconds. How long will it take to pass a platform 650 m long? A.65 sec B.89 sec C.100 sec D.150 sec 5.A train moving at 50 km/hr crosses a bridge in 45 seconds. The length of train is 150 meters. Find the length of the bridge. A.525 m B.545 m C.575 m D.500 m 6Two trains are moving in opposite directions @ 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is: a) 36 b) 45 c) 48 d) 49 7. A jogger running at 9 kmph alongside a railway track in 240 metres ahead of the engine of a 120 metres long train running at 45 kmph in the same direction. In how much time will the train pass the jogger? a) 3.6 sec b) 18 sec c) 36 sec d) 72 sec
8 Two trains, each 100 m long, moving in opposite directions, cross each other in 8 seconds. If one is moving twice as fast the other, then the speed of the faster train is: a) 30 km/hr b) 45 km/hr c) 60 km/hr d) 75 km/hr
9 Two trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time (in seconds) which they take to cross each other, is: a) 9 b) 9.6 c) 10 d) 10.8
10 A train 108 m long moving at a speed of 50 km/hr crosses a train 112 m long coming from opposite direction in 6 seconds. The speed of the second train is: a) 48 km/hr b) 54 km/hr c) 66 km/hr d) 82 km/hr 11 Two trains of equal length are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 seconds. The length of each train is: a) 50 m b) 72 m c) 80 m d) 82 m 1.2 A 270 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train? a) 230 m b) 240 m c) 260 m d) 320 m 13 Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is: a) 1 : 3 b) 3 : 2 c) 3 : 4 d) None of these 14 A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? a) 120 m b) 240 m c) 300 m d) None of these 15) Two stations P and Q are 160 km apart on a straight track. A train starts running from station P at 8 a.m. at a speed of 30 km/hr towards station Q. Another train starts from station Q at 9 a.m. at a speed of 35 km/hr towards station P. At what time they will meet? a) 10 a.m. b) 11 a.m. c) 12 a.m. d) 1 p.m.
