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 = 
TRAINS
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.
Relative speed
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
Average speed
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.
Explanations
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 
Some more Exercises
1. The difference between the time taken by two cars to travel a distance of 250 km is 1h 40 min. The difference between their speeds is 5 kmph.
Quantity I: 25
Quantity II: Speed of slower car
1) If Quantity I = Quantity II or relation can’t to be established from the information that is given
2) If Quantity I < Quantity II
3) If Quantity I >Quantity II
4) If Quantity I < Quantity II
5) If Quantity I > Quantity II
Explanation: According to the question
Quantity I: 25 kmph
Quantity II: Seed of the slower car = 25 kmph
Quantity I = quantity II
Ans: 1
2. The distance between two places P and Q is 600 km. Two persons A and B started towards Q and P from P and Q simultaneously. The speed of A is 25 kmph and speed of B is 35 kmph. They meet at a point M which lies on the way from P to Q.
Quantity I: In how many hours will they be separated by only 480 km before meeting each other.
Quantity II: How long will it take to separate them by 240 km from each other when they cross M (time to be considered after their meeting)
1) If Quantity I = Quantity II or relation can’t
to be established from the information that
is given
2) If Quantity I < Quantity II
3) If Quantity I > Quantity II
4) If Quantity I < Quantity II
5) If Quantity I > Quantity II
Quantity I < Quantity II Ans: 4
3. Two places P and Q are 960 km apart from each other. Two persons start from P towards Q at an interval of 2 hours. Whereas A leaves P for Q before B. The speeds of A and B are 60 kmph and 80 kmph respectively. B overtakes A at M, which is on the way from P to Q.
Quantity I: How long will B take to overtake
Quantity II: What is the extra time required by A to reach at Q?
1) If Quantity I = Quantity II or relation can’t to be established from the information that is given
2) If Quantity I < Quantity II
3) If Quantity I > Quantity II
4) If Quantity I < Quantity II
5) If Quantity I > Quantity II
Extra time required by A to reach at Q = 4 hrs.
: Quantity I > Quantity II Ans: 5
4. Swapna and Sowjanya stay next to each other and study in the same school. Swapna and Sowjanya start walking towards their school at the speed of 2 km/hr and 3 kmph respectively. The faster of the two reaches the school first, turns around and starts walking back. If Swapna and Sowjanya meet 400 m away from the home, what is the distance between their residence and the school?
1) 500m 2) 400m 3) 300m 4) 200m 5) 600m
Explanation: If the time is constant
: Distance between their residence and school is 500m
Ans: 1
5. Suhas and Satvik run on the circular track of 600 m. speed of Suhas and Satvik are 30 m/s and 20 m/s respectively. Initially they are diametrically opposite to each other.
Quantity I: When will they meet for the first time if both move in the same direction.
Quantity II: If both of them move in opposite directions, when will they meet for the third time?
1) If Quantity I = Quantity II or relation can’t to be established from the information that is given
2) If Quantity I < Quantity II
3) If Quantity I > Quantity II
4) If Quantity I < Quantity II
5) If Quantity I > Quantity II
Total time = 30 sec
So, Quantity I = Quantity II Ans: 1
6. Sanjay started for the station half a km from his home walking at 1 km/hr to catch the bus in time. After 6 minutes he realised that he had forgotten a document at home and returned with increased, but constant speed to get it succeeded in catching the bus. Find his latter speed in kmph.
1) 1.5 2) 2 3) 2.5 4) 3 5) 0.5
7. Two cars start together in the same direction from the same place. The first car goes with uniform speed of 2.5 kmph. The second car goes at a speed of 2 kmph in the first hour and increase the speed by 1/2 km/hr in each succeeding hour. After how many hours will the second car overtake the first car if both go non stop?
1) 3 h 2) 6 h 3) 1.5 h 4) 2 h 5) 4 h
8. P and Q start running simultaneously one from point A to B and second from point B to A. P’s speed is 6/5 th of Q’s speed. If after crossing Q, P takes 2 1/2 hours to reach B, how much time does Q take to reach A after crossing P? (in hours)
1) 3 h 36 min 2) 3 h 3) 2 h 4) 4 h 20 min 5) 3 h 30 min
Explanation: After crossing each others, they finish their journey T1 hrs & T2 hrs respectively. Then speed of B is
9. A club owner drives his car from his club to airport at an average speed of 40 mph (miles per hour). At the airport a chopper was waiting for him. He flew from the airport to Bangladesh at an average speed of 50 mph. It took 5 hours for the entire trip. The entire distance he covered was 240 miles. Find the distance from the airport to the club.
1) 50 miles 2) 40 miles 3) 200 miles 4) 180 miles 5) 120 miles
Explanation: Distance between Airport to club = x
Remaining distance by a chopper = 240 − x
10. A bike starts from Delhi every 45 min, the first one starting at 8:30 AM and the last one starting at 5:30 PM. A car starts from Agra every 60 min, the first one starting at 10 AM and the last at 4 PM. A bike takes 5 hrs and a car takes 4 hrs to cover the distance. How many bikes would a car that starts at 2 PM meet on the way?
1) 12 2) 13 3) 14 4) 24 5) 15
Explanation:
