Time, Speed and distance is an important part of every competitive exam. Speed is defined as distance traveled divided by the time. Using this formula all types of problems on speed and distance can be solved. Speed is inversely proportional to the time taken when the distance travelled is constant. So when speed increases time reduces and vice versa. Distance is directly proportional to velocity when time is constant.

# Speed and Distance-Time and Distance- Key Notes

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• Time, Speed and Distance Aptitude basics, practice questions, answers and explanations
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Distance= Speed*time
For a non-uniform motion Average speed= Total distance travelled/Total time taken
When the body travels at 'u' m/s for t1 seconds and 'v' m/s for t2 seconds, then
Average speed= (ut1+vt2)/(t1+t2)
When the body travels l distance at 'u' m/s and 'm' distance at 'v' m/s; Average speed = (mu+lv)/(l+m)

Relative Speed: Speed of a moving body w.r.t. another moving body is called relative speed.

Speed of A w.r.t. B

(i) When they are moving in same direction; Relative speed of A= A-B

(ii) When they are moving in opposite direction; Relative speed of A= A+B

Key points on Trains

When a train is crossing a pole distance travelled by the train= length of train

When a train of length l is crossing a bridge of length b; the distance travelled by train=l+b

When a train of length l is crossing a platform of length p; then distance travelled by train=l+p

When a train of length l1 is crossing/ overtaking another train l2; then distance travelled = l1+l2

Exercise questions

1. Train A traveling at 60 km/hr leaves Mumbai for Delhi at 6 P.M. Train B traveling at 90 km/hr also leaves Mumbai for Delhi at 9 P.M. Train C leaves Delhi for Mumbai at 9 P.M. If all three trains meet at the same time between Mumbai and Delhi, what is the speed of Train C if the distance between Delhi and Mumbai is 1260 kms?
A) 60 km/hr
B) 90 km/hr
C) 120 km/hr
D) 135 km/hr

2. Two trains A and B start simultaneously from stations X and Y towards each other respectively. After meeting at a point between X and Y, train A reaches station Y in 9 hours and train B reaches station X in 4 hours from the time they have met each other. If the speed of train A is 36 km/hr, what is the speed of train B?
A) 24 km/hr
B) 54 km/hr
C) 81 km/hr
D) 16 km/hr

3. A man moves from A to B at the rate of 4 km/hr. Had he moved at the rate of 3.67 km/hr, he would have taken 3 hours more to reach the destination. What is the distance between A and B?
A) 33 kms
B) 132 kms
C) 36 kms
D) 144 kms

4. A man driving his bike at 24 kmph reaches his office 5 minutes late. Had he driven 25% faster on an average he would have reached 4 minutes earlier than the scheduled time. How far is his office?
A) 24 km
B) 72 km
C) 18 km
D) Data Insufficient

5. A man and a woman 81 miles apart from each other, start traveling towards each other at the same time. If the man covers 5 miles per hour to the women's 4 miles per hour, how far will the woman have travelled when they meet?
A) 27
B) 36
C) 45
D) None of these.

6. The speed of a motorboat itself is 20 km/h and the rate of flow of the river is 4 km/h. Moving with the stream the boat went 120 km. What distance will the boat cover during the same time going against the stream?
A) 80 km
B) 180 km
C) 60 km
D) 100 km

7. I travel the first part of my journey at 40 kmph and the second part at 60 kmph and cover the total distance of 240 km to my destination in 5 hours. How long did the first part of my journey last?
A) 4 hours  B) 2 hours  C) 3 hours  D) 2 hours 24 minutes

8. By walking at 3/4th of his usual speed, a man reaches office 20 minutes later than usual. What is his usual time?
A) 30 min
B) 60 min
C) 70 min
D)50 min

9. A passenger train covers the distance between stations X and Y, 50 minutes faster than a goods train. Find this distance if the average speed of the passenger train is 60 kmph and that of goods train is 20 kmph.
A) 20 kms
B) 25 kms
C) 45 kms
D) 40 kms

10. Ram covers a part of the journey at 20 kmph and the balance at 70 kmph taking total of 8 hours to cover the distance of 400 km. How many hours has been driving at 20 kmph?
A) 2 hours
B) 3 hours 20 minutes
C) hours 40 minutes
D)3 hours 12 minutes