**Time and Distance**

**Distance :**

The length of the path travelled by an
object or a body or a person between two places is known as distance. It is
measured in meters or kilometers.

**Speed :**

The distance travelled by any object
or person in unit time is known as the speed of the object or speed of a
person. It is measured in meter per second or kilometer per hour.

Speed =

Distance
Time

Distance = Speed x Time

Time =

Distance
Speed

**Example:**Sameera travelled a distance of 95 kilometres in 5 hours.

Therefore distance travelled by
Sameera in 1 hour =

95
5

= 19 km
Hence,
the speed of Sameera = 19kmph

__Conversion of Units :__**From km/h to m/s :**

To convert the speed of an object from
kmph to mps, multiply the speed by

5
18

.*x kmph = x x*

5
18

mps**Example :**72 kmph = 72 x

5
18

= 20 mps**From m/s to km/h.**

To convert the speed of an object from
mps to kmph, multiply the speed by

18
5

.*x mps= x x*

18
5

kmph**Example :**Convert 30 mps into kmph

30 x

18
5

= 108 kmph**Average Speed :**

If a certain
distance is covered in parts in different time periods, then

Average speed=

Total distance covered
Total time taken

**Example:**A person travels 80 km in 6 hours and the next 30 km in 5 hours. What is his average speed?

Total distance covered = (80 km + 30 km) = 110 km

Total time taken = (6 hours + 5 hours) = 11 hours.

Average Speed =

Total distance covered
Total time taken

=
110
11

= 10 kmph**Average Speed when an object travels equal distances with different speeds:**

**1.**If a person covers two equal distances with the speed of x and y units respectively, then the average speed of the man for complete journey =

2xy
(x+y)

**Example:**John covers half of the distance with speed of 40 kmph and the remaining half of the distance with speed of 60 kmph. What is his average speed?

Answer : He travelled two equal
distance with speeds 40kmph and 60kmph

Average Speed =

2 x 40 x 60
(40+60)

= 48 kmph**2.**A person travels 3 equal distances with speeds x, y and z units, then his average speed =

3xyz
(xy+yz+zx)

**Example :**Sudheer travels 1/3

^{rd}of his journey at 10 km/h , next 1/3

^{rd}at 30km/h and remaining 1/3

^{rd}at 60km/h. What is his average speed during the journey?

a)15 km/h b)20 km/h c)25km/h d)30km/h

Answer :Sudheer travels 3 equal distances at speeds of 10 kmph, 20
kmph and 30 kmph

Average Speed =

3xyz
(xy+yz+zx)

=

(3 x 10 x 30 x 60 )
(10 x 30) + (30 x 60) + (60 x 10)

= 20 kmph

__Concept of Relative Speed :__**If two objects are moving in the same direction at speeds of x and y, then their relative speed = (x-y)**

__Objects moving in the same direction:__
For example, if the two bikes A and B
move in the same direction at speeds of 50 kmph and 40 kmph , then the relative
speed of A with respect to B is (50-40)=10 kmph.

**Example :**Ravi and Raju start walking in the same direction at 12 km/h and 10 km/h, respectively. In how many hours will they be 16km apart?

a)4 hours b)5 hours c)6
hours d)8 hours

Answer : Time =

Distance
Speed

Here both are moving in the same direction, so the relative speed
is (12-10) = 2 kmph

Time =

16
2

= 8 hours

__Objects are moving in the opposite direction :__**If two objects are moving in opposite directions at speeds of x and y, then their relative speed = (x+y).**

If two cars are travelling towards each other at speeds of 30 kmph
and 40 kmph respectively, then their relative speed = (30+40) = 70 kmph.

**Example :**Sameera and Sravani walking in opposite directions at 12km/h and 10 km/h, respectively. In how many hours will they be 66 km apart?

a)6 hours b)33 hours c)3
hours d)5 hours

**Answer :**Sameera and Sravani are walking in the opposite direction , their relative speed is the sum of their speeds = (12+10) =22 kmph

Time =

Distance
Time

=
66
22

= 3 hours**Note :**The ratio of speeds of two objects is a:b, then to cover the same distance, the ratio of time taken will be b:a

**Example :**The ratio of the speeds of two persons to cover a distance is 4:5, then the ratio of time taken by them to cover the same distance will be 5 :4.

**Example**

**:**The ratio between the speeds of A and B is 5 :7, and A takes 35 minutes to cover a distance. In what time does B cover the same distance?

a)10
min b)15 min c)25 min

**d)30min**
Answer :
The ratio of between the speeds of A and B is 5:7

Then ratio of the times taken by A and B =
7:5

Time taken by A to cover a distance is 7x =
35 minutes

Therefore, time taken by B to cover same
distance = 5x = 5x5 = 25 minutes