Time and Distance - Arithmetic

Distance

The length of path covered by an object is called DISTANCE.

Distance is generally denoted by "S" or "s" or "D" or "d".

The SI unit of distance is "meter" and denoted by "m". The long distance is measured in "Kilo Meter" and abbreviated as "Km".

1000 meter = 1 kilo meter

Time

Time taken to cover a particular distance is known as "TIME".

Time is generally denoted by "t" or "T".

The SI unit of time is "second".

1 hour = 60 minute

1 minute = 60 second

Speed

The distance covered in unit time is called "SPEED".

Speed is generally denoted by "v".

Important Formula

Distance = Time × Speed

Time =

Speed =

Average Speed =

Solved Examples

Calculation of distance when speed and time are given.

Question (1) How much distance is covered by a cyclist running at a speed of 5 km/hour in 3 hour?

Solution

Given, Speed of the cyclist (v) = 5 km/hour

Time (t) = 3 hour

Thus, distance (s) = ?

We know that,

Distance = Speed × Time

= 5 km/h × 3 h

= 15 km

Thus, distance covered by the cyclist in given time = 15 km Answer

Alternate Method (Unitary method)

As given, the speed of the cyclist = 5 km/hour

This means the cyclist covers 5 km in 1 hour.

∵ The distance covered by the cyclist in 1 hour = 5 km

∴ The distance covered by the cyclist in 3 hour = 5 km × 3

= 15 km

Thus, distance covered by the cyclist in given time = 15 km Answer

Question (2) The speed of a car is 15 km/hour. Find the distance covered by the given car in 5 hour.

Solution

Given, Speed of the car (v) = 15 km/hour

Time (t) = 5 hour

Thus, distance (s) = ?

We know that,

Distance = Speed × Time

= 15 km/h × 5 h

= 75 km

Thus, distance covered by the car in given time = 15 km Answer

Alternate Method (Unitary method)

As given, the speed of the car = 15 km/hour

This means the car covers a distance of 15 km in 1 hour.

∵ The distance covered by the car in 1 hour = 15 km

∴ The distance covered by the car in 5 hour = 15 km × 5

= 75 km

Thus, distance covered by the car in given time = 75 km Answer

Question (3) A car runs for 20 hour. If the speed of the car is 60 km per hour, the what distance the car will cover in the given time?

Solution

Given, Speed of the car (v) = 60 km/hour

Time (t) = 20 hour

Thus, distance (s) = ?

We know that,

Distance = Speed × Time

= 60 km/h × 20 h

= 1200 km

Thus, distance covered by the car in given time = 1200 km Answer

Alternate Method (Unitary method)

As given, the speed of the car = 60 km/hour

This means the car covers a distance of 60 km in 1 hour.

∵ The distance covered by the car in 1 hour = 60 km

∴ The distance covered by the car in 20 hour = 60 km × 20

= 1200 km

Thus, distance covered by the car in given time = 1200 km Answer

Question (4) A man walks 6 km in 1 hour. If the man walks for 5 hour, the what distance will he covered?

Solution

Given, the man walks 6 km in 1 hour.

We know that speed is the distance covered in unit time.

Thus, speed of the man (v) = 6 km/hour

Time (t) = 5 hour

Thus, distance (s) = ?

We know that,

Distance = Speed × Time

= 6 km/h × 5 h

= 30 km

Thus, distance covered by the man in the given time = 30 km Answer

Alternate Method (Unitary method)

As given, the man covers a distance of 6 km in 1 hour.

∵ The distance covered by the man in 1 hour = 6 km

∴ The distance covered by the man in 5 hour = 6 km × 5

= 30 km

Thus, distance covered by the man in given time = 30 km Answer

Question (5) What distance will be covered by a car at a speed of 45 km/h in 9 hour?

Solution

Given, Speed of the car (v) = 45 km/hour

Time (t) = 9 hour

Thus, distance (s) = ?

We know that,

Distance = Speed × Time

= 45 km/h × 9 h

= 405 km

Thus, distance covered by the car in given time = 405 km Answer

Alternate Method (Unitary method)

As given, the speed of the car = 45 km/hour

This means the car covers a distance of 45 km in 1 hour.

∵ The distance covered by the car in 1 hour = 45 km

∴ The distance covered by the car in 9 hour = 45 km × 9

= 405 km

Thus, distance covered by the car in the given time = 405 km Answer

Question (6) Calculate the distance covered by a bus at a speed of 50 km/h in 5 hour.

Solution

Given, Speed of the bus (v) = 50 km/hour

Time (t) = 5 hour

Thus, distance (s) = ?

We know that,

Distance = Speed × Time

= 50 km/h × 5 h

= 250 km

Thus, distance covered by the bus in given time = 250 km Answer

Alternate Method (Unitary method)

As given, the speed of the bus = 50 km/hour

This means the bus covers a distance of 50 km in 1 hour.

∵ The distance covered by the bus in 1 hour = 50 km

∴ The distance covered by the bus in 5 hour = 50 km × 5

= 250 km

Thus, distance covered by the bus in the given time = 250 km Answer

Question (7) Calculate the distance covered by a bus at a speed of 40 km/h in 15 hour.

Solution

Given, Speed of the bus (v) = 40 km/hour

Time (t) = 15 hour

Thus, distance (s) = ?

We know that,

Distance = Speed × Time

= 40 km/h × 15 h

= 600 km

Thus, distance covered by the bus in given time = 600 km Answer

Alternate Method (Unitary method)

As given, the speed of the bus = 40 km/hour

This means the bus covers a distance of 40 km in 1 hour.

∵ The distance covered by the bus in 1 hour = 40 km

∴ The distance covered by the bus in 15 hour = 40 km × 15

= 600 km

Thus, distance covered by the bus in the given time = 600 km Answer