# Worksheet on Relative Speed | Relative Speed Practice Worksheets with Solutions

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When two train passes a moving object with some length in the opposite direction. Let the length of the faster train be m meters and the length of the slower train be n meters. Speed of faster train be x km/hr and speed of slower train be y km/hr

Relative speed = (x + y) km/hr

When two train passes a moving object with some length in the same direction. Let the length of the faster train be m meters and the length of the slower train be n meters. Speed of faster train be x km/hr and speed of slower train be y km/hr

Relative speed = (x – y) km/hr

1. Two persons are running from the same place at a speed of 6 km/hr and 3 km. Find the distance between them after 3 minutes if they are moving in the opposite directions.

Solution:

Given that Two persons are running from the same place at a speed of 6 km/hr and 3 km/hr.
The speed of a first-person is 6 km/hr.
The speed of the second person is 3 km/hr.
As the two persons moving in opposite directions, the speeds are added.
Relative Speed = 6 km/hr + 3 km/hr = 9 km/hr.
Given that the time = 3 minutes.
Convert the time from minutes to hours.
Divide minutes with 60 to convert minutes to hours.
3 minutes = 3/60 hours
3 minutes = 1/20 hours.
Let us find the distance between two persons.
Distance = Speed × Time
Distance = 9 km/hr × 1/20 hrs
Distance = 9/20 km.

The distance between two persons when they are moving each other in opposite directions is 9/20 km.

2. Two boys are running in the same direction from the same place at the speed of 20 km/hr and 12 km/hr. Find the distance between them after 40 minutes.

Solution:

Given that Two boys are running in the same direction from the same place at the speed of 20 km/hr and 12 km/hr.
The speed of a first-person is 20 km/hr.
The speed of the second person is 12 km/hr.
As the two boys moving in the same direction, the speeds are subtracted.
Relative Speed = 20 km/hr – 12 km/hr = 8 km/hr.
Given that the time = 40 minutes.
Convert the time from minutes to hours.
Divide minutes with 60 to convert minutes to hours.
40 minutes = 40/60 hours
40 minutes = 2/3 hours.
Let us find the distance between two persons.
Distance = Speed × Time
Distance = 8 km/hr × 2/3 hours.
Distance = 16/3 km.

The distance between two boys running in the same direction from the same place is 16/3 km.

3.  A train 70 m long is running at a speed of 40 km/hr. In what time will it pass a man who is running at speed of 4 km/hr in the same direction in which the train is moving.

Solution:

Given that a train 70 m long is running at a speed of 40 km/hr.
The man running at a speed of 4 km/hr in the same direction.
As the train and man are moving in the same direction, the speeds are subtracted.
Relative Speed = 40 km/hr – 4 km/hr = 36 km/hr.
Given that the distance = 70 m.
Now, find the speed of the train in m/sec.
convert km/hr into m/sec.
Multiply km/hr with 5/18 to convert it into m/sec.
km/hr × 5/18 = m/sec
36 km/hr × 5/18 = 10 m/sec.
Distance = Speed × Time
Time = Distance/Speed
Time = 70 m/10 m/sec
Time = 7 sec

The train passes a man who is running at speed of 4 km/hr in the same direction in 7 sec.

4. A train 75 m long is running at a speed of 33 km/hr. In what time will it pass a man who is running at the speed of 3 km/hr in the opposite direction in which the train is moving?

Solution:

Given that a train 75 m long is running at a speed of 33 km/hr.
The man running at a speed of 3 km/hr in the opposite direction.
As the train and man are moving in the opposite direction, the speeds are added.
Relative Speed = 33 km/hr + 3 km/hr = 36 km/hr.
Given that the distance = 75 m.
Now, find the speed of the train in m/sec.
convert km/hr into m/sec.
Multiply km/hr with 5/18 to convert it into m/sec.
km/hr × 5/18 = m/sec
75 km/hr × 5/18 = 20.833 m/sec.
Distance = Speed × Time
Time = Distance/Speed
Time = 75 m/20.833 m/sec
Time = 3.6 sec

The train passes a man who is running at speed of 4 km/hr in the opposite direction in 3.6 sec.

5. Two trains of length 120 m and 80 m respectively are running at the speed of 30 km/hr and 20 km/hr on parallel tracks in the opposite direction. In what time will they cross each other?

Solution:

Given that Two trains of length 120 m and 80 m respectively are running at the speed of 30 km/hr and 20 km/hr on parallel tracks in the opposite direction.
As the two trains are moving in the opposite direction, the speeds are added.
Relative Speed = 30 km/hr + 20 km/hr = 50 km/hr.
Distance = (120 m – 80 m) = 40 m.
Now, find the speed of the train in m/sec.
convert km/hr into m/sec.
Multiply km/hr with 5/18 to convert it into m/sec.
km/hr × 5/18 = m/sec
50 km/hr × 5/18 = 13.888 m/sec.
Distance = Speed × Time
Time = Distance/Speed
Time = 40 m/13.888 m/sec
Time = 2.88 sec

The two trains take 2.88 sec to cross each other.

6. Two trains 65 m and 125 m long are running on parallel tracks in the same direction with a speed of 40 km/hr and 35 km/hr respectively. How long will they take to clear off each other from the moment they meet?

Solution:

Given that Two trains of length 65 m and 125 m long are running on parallel tracks in the same direction with a speed of 35 km/hr and 40 km/hr respectively.
As the two trains are moving in the same direction, the speeds are subtracted.
Relative Speed = 40 km/hr – 35 km/hr = 5 km/hr.
Distance = (65 m + 125 m) = 190 m.
Now, find the speed of the train in m/sec.
convert km/hr into m/sec.
Multiply km/hr with 5/18 to convert it into m/sec.
km/hr × 5/18 = m/sec
5 km/hr × 5/18 = 1.388 m/sec.
Distance = Speed × Time
Time = Distance/Speed
Time = 190 m/1.3888 m/sec
Time = 136.8 sec

The two trains take 136.8 sec to clear off each other from the moment they meet.

7. Two trains are running on parallel tracks in the same direction at 20 km/hr and 15 km/hr respectively. The faster train passed a man than the slower train in 72 seconds. Find the length of the faster train?

Solution:

Given that Two trains are running on parallel tracks in the same direction at 20 km/hr and 15 km/hr respectively. The faster train passed a man than the slower train in 72 seconds.
As the two trains are running on parallel tracks in the same direction, the speeds are subtracted.
Relative Speed = 20 km/hr – 15 km/hr = 5 km/hr.
Now, find the speed of the train in m/sec.
convert km/hr into m/sec.
Multiply km/hr with 5/18 to convert it into m/sec.
km/hr × 5/18 = m/sec
5 km/hr × 5/18 = 1.388 m/sec.
Distance = Speed × Time
Distance = 1.388 m/sec × 72 seconds = 100 sec

The length of the faster train is 100 sec.