**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 kilometres.

**Speed :**

The
distance travelled by any object or person in unit time is knows as speed of
the object or speed of a person. It is measured in meter per second or kilometre
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
her in 1 hour =

95
25

= 19 km
Hence,
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 :**

**It is certain distance is covered in parts at different speeds .**

Average
speed=

Total Distance Covered
Total Time Taken

**Example :**A person travels 80 km in 6 hours and 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 a half of the distance with speed of 40 kmph and 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

**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

of his journey at 10 km/h ,
next
1
3

at 30km/h and remaining
1
3

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
10x30 + 30+60 + 60+10

= 20 kmph

**Concept of Relative Speed :**

**Objects moving in the same direction :**If two objects are moving in same direction at speeds of x and y , then their relative speed = x-y

For
example, if the two bikes A and B move in the same direction at speeds of
520kmph and 40 kmph , then their relative speed of A with respect to B is
(50-40)=10 kmph.

**Example :**Ravi and Raju start walking in the same direction at 12km/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 same direction, so
the relative speed is 12-10 = 2 kmph

Time =

16
2

= 8 hours**Objects moving in 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 opposite direction , their relative speed is 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 same distance, the ratio of time taken will be b:a****Example :**The ratio of the speeds of two person to cover a distance is 4:5, then the ratio of time taken by them to cover 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 covers 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