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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 dista...

# Aptitude Questions and Answers - Time and Distance - Concept and Formulae

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 1/3rd of his journey at 10 km/h , next 1/3rd   at 30km/h and remaining 1/3rd  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 :

Objects moving in the same direction: If two objects are moving in the 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 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
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