Time, Speed and Distance
Concepts:
1. 
Relationship between speed, distance and time: 
Speed = Distance / Time 

OR 

Distance = Speed* Time 

2. 
Average Speed = 2xy / x+y 
x is the (km/hr) speed for certain distance and 

y is the (km/hr) speed at for same distance. 

NOTE: 





Conversion of km/ hr to m/ sec i.e.., x km/ hr = (x* 5/18) m/sec, similarly, x m/sec = (x*18/5) km/sec 

3. 
If in questions Distance is constant then, 
Speed = Distance/ Time 

speed will be inversely proportional to time i.e.., If speed increases then time take to reach the destination will decrease and vice versa. 

Problems 

1. 
A man covers a distance of 700m in 1min 10sec. What will be the speed in km/hr? 
Solution: Speed =Distance / Time 

Distance covered = 700m, Time taken = 1min 10sec = 70sec 

Therefore, Speed= 700 / 70 = 10 m/sec 

10m/sec = (10*18/5) km/hr = 36 km/ hr. 

2. 
A boy travelling from his home to school at 25 km/hr and came back at 4 km/hr. If whole journey took 5 hours 48 min. Find the distance of school from home? 
Solution: In this question, distance for both speed is constant. 

Average speed = (2xy/ x+y) km/hr, where x and y are speeds 

Average speed = (2*25*4)/ 25+4 =200/29 km/hr 

Time = 5hours 48min= 29/5 hours 

Now, Distance travelled = Average speed * Time 

Distance Travelled = (200/29)*(29/5) = 40 km 

Therefore distance of school from home = 40/2 = 20km. 

3. 
Two men start from opposite ends A and B of a linear track respectively and meet at point 80m from A. If AB is 100m. What will be the ratio of speed of both men? 
Solution: Time is constant in this question. Therefore, speed is directly proportional to distance(Speed∝Distance) 



Ratio of distance covered by both men = 80:20 = 4:1 

Therefore, Ratio of speeds of both men = 4:1 

4. 
A car travels along four sides of a square at speeds of 100, 200, 400 and 800 km/hr. Find average speed. 
Solution: Let x km be the side of square and y km/hr be average speed 

Using basic formula, Time = Total Distance / Average Spee 

x/100 + x/200 + x/400 + x/800 = 4x/y ⇒ 15x/ 800 = 4x/ y⇒ y=213.3 

Average speed = 213.3 km/hr 