The relation among distance, time and speed is
Distance = Speed x Time.
If a car covers 50 kilometres in each hour then the speed of the car is 50Kmph.
If a man travels 10 metres in one second’s time the the speed of the man is 10 mps.
Convertion of speeds: KMPH to MPS
MPS to KMPH
When a certain distance is traveled with a speed of x kmph and another equal distance is traveled at y kmph, then the average speed =
If a train has to cross a pole or a man or any particular point then it has to cover a distance equal to its own length.
If a train has to cross a platform or bridge or tunnel etc. then it has to cover a length equal to its length + platform/bridge/tunnel length.
When two speeds are in opposite direction,
Relative speed = sum of the speeds.
When two speeds are in the same direction,
Relative speed = difference of the speeds.
BOATS AND STREAMS
Still water: water without motion. A boat can travel or a man can swim in that water with their original speeds.
Stream / current : water flow with some speed.
Down stream: along with the flow.
Upstream: against the water flow
If the speed of the boat in still water is b kmph and speed of the current is c kmph respectively, then
Downrate ( x ) = b + c
Uprate ( y ) = b – c
If a moving object travels from A to B at the speed of x km/hr, and from B to A at the speed of y km/hr, then
Example 1: A train 100 metre long is running at the speed of 21 km/hr and another train 150 meter long is running at the speed of 36 km/hr in the same direction. How long will the faster train take to pass the first train?
Solution: Sum of the length of both the train = x1 + x2 = 100 + 150 = 250 m
Difference of their speeds = y1 - y2 = 21 - 36
= 15 km/hr
Question with office concern
Example 1: A person walking at x km/hr reaches his office t1 minutes late. If he walks at y km/hr, he reaches there t2 minutes earlier, then
Example 5: A man covers a distance of 160 km at 64 km/hr and next 160 km at 80 km/hr. what is his average speed for his whole journey of 320 km?
Example 6: What will be the length of the train P when it is running at 60 km/hr and crosses another train Q running in opposite direction, in 18 seconds? In order to answer this question which of the statements (a) and (b) is/are sufficient?
(a) Length of the train Q is 80 meter
(b) Speed of the train Q is 90 km/hr
Solution: Both statements (a) and (b) together are necessary
∵ The trains are running in opposite directions
Example 7: A boat takes 3 hours to go from P to Q downstream and from Q to P up stream. What is the speed of the boat in still water? to know the answer of this question, the knowledge of which of the statements (a) and (b) is/are sufficient?
The distance between P and Q is 6 km.
The speed of the river is 2 km/hr.
Solution: Both statements (a) and (b) together are necessary to the question.
Let the speed of the boat in still water be x km/hr.
∴ Speed of the boat down stream = (x + 2) km/hr
And Speed of the boat upstream = (x -2) km/hr
Now x can be calculated.
Some more Exercises
1. A 150 m long train running at 36 kmph speed crosses a bridge in 27 sec. Find the length of the bridge.
1) 75 m 2) 100 m 3) 120 m 4) 85 m 5) None of these
2. Two trains 125 m and 95 m long are running in opposite directions with speeds of 40 kmph and 32 kmph respectively. In what time will they completely clear each other from the moment they meet?
1) 20 sec 2) 11 sec 3) 22 sec 4) 15 sec 5) None of these
3. A train crosses a bridge of length 290 metres in 27 seconds. Find the length of the train if it runs at 90 kmph speed.
1) 385 m 2) 270 m 3) 245 m 4) 675 m 5) None of these
4. A boat covers 162 km upstream in 6 hours. If the speed of the current of the stream is 3 kmph, find the speed of the boat.
1) 30 kmph 2) 24 kmph 3) 32 kmph 4) 18 kmph 5) None of these
5. In what time, a 178 m long train running at 108 kmph speed, overtakes a 247 m long train running at 36 kmph rate?
1) 10.625 sec 2) 21.25 sec 3) 20.45 sec 4) 19.75 sec 5) None of these
6. If a car travels at 5/8 th of its original speed, it takes 12 minutes more time to cover a certain distance. Find the actual time it takes to cover that distance?
1) 36 min 2) 24 min 3) 18 min 4) 20 min 5) None of these
7. A train crosses a bridge of length 800 m in 100 seconds and a platform of length of 400 m in 60 seconds. Find the length of the train.
1) 80 m 2)100 m 3) 200 m 4) Can’t be determined 5) None of these
8. Speed of a boat is 8 kmph. It goes to a distance from A to B upstream and comes back from B to A downstream in 24 hours. If the speed of the current is 2 kmph, find the distance between A and B.
1) 60 km 2) 75 km 3) 40 km 4) 90 km 5) None of these
9. A man goes from his house to office in a car. If his speed is 60 kmph, he reaches his office 3 minutes late however if his speed is 80 kmph he is early by 5 minutes. Find the distance between his house and office.
1) 32 km 2) 25 km 3) 60 km 4) Can’t be determined 5) None of these
10. A man covers 220 km in 8 hours and another 300 km at an average speed of 60 kmph. Find the average speed of the man for the total distance.
1) 43.75 kmph 2) 55 kmph 3) 45 kmph 4) 40 kmph 5) None of these
11. A train running at a speed of 65 kmph passes a man, who is sitting in another train running at 38 kmph in the same direction in 16 seconds. Find the length of the faster train.
1) 135 m 2)120 m 3) 180 m 4) Data Inadequate 5) None of these
12. A runs 200 metres in 40 seconds and B runs the same distance in 50 seconds. By what distance will A beat B in a race of 100 metres?
1) 40 m 2) 25 m 3) 10 m 4) 15 m 5) 20 m
13. A boat covers 60 km distance downstream or 36 km distance upstream in the same time. If the speed of the current is 3 kmph, find the speed of the boat.
1) 48 kmph 2) 12 kmph 3) 16 kmph 4) 15 kmph 5) None of these
14. A man covers a distance of 270 km at 90 km/hr and next 270 km at 60 km/hr. What is his average speed for his whole journey of 540 km?
1) 75 kmph 2) 68 kmph 3) 72 kmph 4) 85 kmph 5) None of these
Answers: 1-3; 2-2; 3-1; 4-1; 5-2; 6-4; 7-3; 8-4; 9-1; 10-4; 11-2; 12-5; 13-2; 14-3.
1. Let the length of the platform be ‘x’ metres Distance = (150 + x) m, Speed = 36 kmph = 36 × 5/18 = 10 mps,
Time = 26 Sec; Distance = Speed × Time
⇒ 150 + x = 10 mps × 27 sec
⇒ 150 + x = 270 m
⇒ x = 120 m
2. Total Distance = (125 + 95) = 220 m Relative Speed = 40 + 32 = 72 kmph = 72 × 5/18 = 20 mps.
Required Time = 220/20 = 11 sec
3. Let the length of the bridge be ‘x’ metres
∴ (290 + x) m = 90 × 5/18 mps × 27 sec
⇒ 290 + x = 675 m ⇒ x = 385 m
4. Speed = 162 km /6 hrs = 27 kmph
∴ upstream = 27 kmph
Boat - Current = 27 kmph
Boat - 3 = 27 ⇒ Boat = 30 kmph
5. Required time is (178 + 247)m/(108 - 36) kmph
(overtaking means same direction)
⇒ 425m/72 × 5/18 mps = 425m/ 20 mps = 21.25 sec.
6. Let the actual speed be's kmph and time be ‘t’ hours
1. A car covers a certain distance. The average speed of the car for the first half is 80 km/hr and the average speed for the next half is 120 km/hr. what is the average speed of the car for the entire distance?
A) 100 kmph B) 78 kmph C) 96 kmph D) 90 kmph
2. A man covers 220 km in 8 hours and another 300 km at an average speed of 60 kmph. Find the average speed of the man for the total distance.
A) 43.75 kmph B) 55 kmph C) 45 kmph D) 40 kmph
3. Two trains 125 m and 95 m long are running in opposite directions with speeds of 40 kmph and 32 kmph respectively. In what time will they completely clear each other from the moment they meet?
A) 10 sec B) 12 sec C) 11 sec D) 15 sec
4. Two trains start from a certain place on two parallel tracks in the same direction. The speed of the trains are 45 km/hr and 40 km/hr respectively. The distance between the two trains after 45 minutes will be (SSC-CGL 2016)
A) 2.5 km B) 2.75 km C) 3.7 km D) 3.75 km
5. Two cars start from A and B respectively and moves in opposite directions towards B and A at average speeds 44 kmph and 40 kmph respectively. After what time will they be 294 km apart?
A) 3.5 hours B) 4.5 hours C) 4 hours D) 3 hours
6. The time for a train of length 110 meters running at the speed of 72 km/hr to cross a bridge of length 132 meters is (SSC-CGL 2016)
A) 9.8 sec B) 12.1 sec C) 12.42 sec D) 14.3 sec
7. The distance between two stations A and B is 428 km. A train starts from station A at 6 am and moves towards station B at an average speed of 48 kmph. Another train starts from station B at 6.20 am and moves towards station A at an average speed of 55 kmph. At what time will the trains meet? (SSC-CGL 2019)
A) 9.40 am B) 10.20 am C) 10.40 am D) 10 am
8. The distance between two stations A and B is 575 km. A train starts from station A at 3 pm and moves towards station B at an average speed of 50 kmph. Another train starts from station B at 3.30 pm and moves towards station A at an average speed of 60 kmph. How far from station A will the trains meet? (SSC-CGL 2019)
A) 275 km B) 225 km C) 300 km D) 325 km
9. A thief steals a car at 2 pm and runs away at a speed of 60 kmph. The theft was noticed at 3pm and the policeman started chasing in another car at a speed of 75 kmph. At what time can the police man catch the thief?
A) 9 pm B) 7.30 pm C) 7 pm D) 8 pm
10. Two cars A and B leave Delhi at 8.30 am and at 9 am for Shimla respectively. They travel at the speeds of 40 kmph and 50 kmph respectively. How many kilometres away from Delhi will the two cars be together? (SSC-CGL 2019)
A) 45 km B) 5 km C) 200 km D) 100 km
11. A boat covers 78 km down stream or 30 km upstream in the same time. If the speed of the current is 4 kmph, what is the speed of the boat?
A) 18 kmph B) 13 kmph C) 5 kmph D) 9 kmph
12. In a stream running at 3 kmph, a motor boat goes 12 km upstream and back to the starting point in 60 min. find the speed of the motor boat in still water (in kmph) (SSC-CGL 2019)
A) 2(2 + √17) B) 2(4 + √15) C) 3(2 + √17) D) 3(4 + √17)