Question 1

Two trains are running towards each other on parallel tracks. Train A is moving at 60 km/h and Train B is moving at 40 km/h. If they are currently 500 km apart, in how many hours will they meet?

Accepted Answer

Step 1: When two objects move towards each other, their relative speed is the sum of their individual speeds. Step 2: Relative speed = 60 + 40 = 100 km/h. Step 3: Time = Distance ÷ Relative speed = 500 ÷ 100 = 5 hours. Therefore, the trains will meet in 5 hours.

Question 2

Two trains A and B start simultaneously from opposite ends of a 360 km track. Train A travels at 60 km/h and Train B travels at 90 km/h. After how many hours will they meet?

Accepted Answer

Step 1: When two objects move towards each other, their relative speed is the sum of their individual speeds.
Relative speed = 60 + 90 = 150 km/h

Step 2: Use the formula: Time = Distance / Relative Speed
Time = 360 / 150 = 2.4 hours

Step 3: Converting to hours and minutes: 2.4 hours = 2 hours 24 minutes
Or in decimal form: 2.4 hours

Therefore, the trains will meet after 2.4 hours (or 2 hours 24 minutes).

Question 3

Two trains are running towards each other on parallel tracks. Train A is moving at 60 km/h and Train B is moving at 40 km/h. If they are currently 500 km apart, in how many hours will they meet?

Accepted Answer

Step 1: When two objects move towards each other, their relative speed is the sum of their individual speeds. Step 2: Relative speed = 60 + 40 = 100 km/h. Step 3: Time = Distance ÷ Relative speed = 500 ÷ 100 = 5 hours. Therefore, the trains will meet in 5 hours.

Question 4

Two trains start simultaneously from stations A and B, which are 360 km apart. Train X travels from A to B at 80 km/h, while Train Y travels from B to A at 100 km/h. At what distance from station A will the two trains meet?

Accepted Answer

Step 1: When two objects move towards each other, their relative speed = Sum of individual speeds = 80 + 100 = 180 km/h.

Step 2: Time taken to meet = Total distance / Relative speed = 360 / 180 = 2 hours.

Step 3: Distance covered by Train X from station A in 2 hours = Speed × Time = 80 × 2 = 160 km.

Therefore, the trains will meet at 160 km from station A.

Question 5

Two trains start simultaneously from stations A and B, which are 360 km apart. Train X travels from A towards B at 60 km/h, while Train Y travels from B towards A at 90 km/h. At what time will they meet, and how far will Train X have travelled by then?

Accepted Answer

Step 1: When two objects move towards each other, their relative speed is the sum of their individual speeds. Relative speed = 60 + 90 = 150 km/h. Step 2: Time to meet = Distance ÷ Relative speed = 360 ÷ 150 = 2.4 hours = 2 hours 24 minutes. Step 3: Distance travelled by Train X = Speed of X × Time = 60 × 2.4 = 144 km. Therefore, Train X travels 144 km.

Question 6

Two trains start simultaneously from stations A and B, which are 360 km apart. Train X travels from A towards B at 60 km/h, while Train Y travels from B towards A at 90 km/h. At what time will they meet, and how far will Train X have travelled by then?

Accepted Answer

Step 1: When two objects move towards each other, their relative speed = sum of individual speeds = 60 + 90 = 150 km/h. Step 2: Time to meet = Total distance ÷ Relative speed = 360 ÷ 150 = 2.4 hours. Step 3: Distance travelled by Train X = Speed of X × Time = 60 × 2.4 = 144 km. Therefore, the answer is 144 km.

Question 7

Two trains start simultaneously from stations A and B, which are 480 km apart. Train X travels from A towards B at 60 km/h, while Train Y travels from B towards A at 40 km/h. After how much time will they meet, and at what distance from station A will they meet?

Accepted Answer

Step 1: When two objects move towards each other, their relative speed is the sum of their individual speeds. Relative speed = 60 + 40 = 100 km/h. Step 2: Time to meet = Total distance ÷ Relative speed = 480 ÷ 100 = 4.8 hours. Step 3: Distance from A = Speed of Train X × Time = 60 × 4.8 = 288 km. Therefore, they meet after 4.8 hours at 288 km from station A.

Question 8

Two trains start simultaneously from stations A and B, which are 480 km apart. Train X travels from A towards B at 60 km/h, while Train Y travels from B towards A at 40 km/h. After how much time will they meet, and at that moment, how much farther will Train X have travelled compared to Train Y?

Accepted Answer

Step 1: When two objects move towards each other, their relative speed = 60 + 40 = 100 km/h. Step 2: Time to meet = Total distance ÷ Relative speed = 480 ÷ 100 = 4.8 hours. Step 3: Distance travelled by Train X = 60 × 4.8 = 288 km. Step 4: Distance travelled by Train Y = 40 × 4.8 = 192 km. Step 5: Difference = 288 − 192 = 96 km. Therefore, Train X travels 96 km farther than Train Y.

Question 9

A boat travels downstream at 18 km/h and upstream at 12 km/h. What is the speed of the boat in still water?

Accepted Answer

Step 1: Let the speed of the boat in still water be B and the speed of the current be C. Step 2: Downstream speed = B + C = 18 km/h. Step 3: Upstream speed = B − C = 12 km/h. Step 4: Adding both equations: 2B = 30, so B = 15 km/h.

Question 10

A boat travels 48 km downstream in 3 hours. If the speed of the current is 2 km/h, what is the speed of the boat in still water?

Accepted Answer

Step 1: Downstream speed = Distance ÷ Time = 48 ÷ 3 = 16 km/h. Step 2: Downstream speed = Speed of boat + Speed of current. Therefore, 16 = Speed of boat + 2. Step 3: Speed of boat in still water = 16 − 2 = 14 km/h. Therefore, the answer is 14 km/h.

Question 11

Two trains are moving towards each other on parallel tracks. Train A travels at 60 km/h and Train B travels at 40 km/h. If they are initially 300 km apart, how long will it take for them to meet?

Accepted Answer

Step 1: When two objects move towards each other, their relative speed is the sum of their individual speeds. Relative speed = 60 + 40 = 100 km/h. Step 2: Time = Distance ÷ Relative speed = 300 ÷ 100 = 3 hours. Therefore, the answer is 3 hours.

Question 12

Two runners start from opposite ends of a 400-meter track and run towards each other. Runner X runs at 8 m/s and Runner Y at 12 m/s. In how many seconds will they meet?

Accepted Answer

Step 1: When two objects move towards each other, relative speed is the sum of their individual speeds. Step 2: Relative speed = 8 + 12 = 20 m/s. Step 3: Time = Distance ÷ Relative speed = 400 ÷ 20 = 20 seconds.

Question 13

Two trains are moving towards each other on parallel tracks. Train A travels at 60 km/h and Train B travels at 40 km/h. If they are initially 500 km apart, in how many hours will they meet?

Accepted Answer

Step 1: When two objects move towards each other, their relative speed is the sum of their individual speeds. Step 2: Relative speed = 60 + 40 = 100 km/h. Step 3: Time = Distance ÷ Relative speed = 500 ÷ 100 = 5 hours.

Question 14

A car travels at 80 km/h and a motorcycle travels at 60 km/h in the same direction. If the motorcycle is currently 40 km ahead of the car, how long will it take for the car to catch up?

Accepted Answer

Step 1: Relative speed = Speed of car - Speed of motorcycle = 80 - 60 = 20 km/h. Step 2: Time = Distance ÷ Relative Speed = 40 ÷ 20 = 2 hours.

Question 15

Two runners start from the same point and run in opposite directions. Runner A runs at 12 km/h and Runner B runs at 8 km/h. After how many hours will they be 60 km apart?

Accepted Answer

Step 1: When two objects move in opposite directions, their relative speed is the sum of their speeds. Relative speed = 12 + 8 = 20 km/h. Step 2: Time = Distance ÷ Relative Speed = 60 ÷ 20 = 3 hours.

Question 16

A man cycles at 15 km/h and a woman cycles at 10 km/h in the same direction on the same road. If the man is currently 20 km behind the woman, how long will it take for the man to catch up with the woman?

Accepted Answer

Step 1: When two objects move in the same direction, their relative speed is the difference of their speeds. Relative speed = 15 - 10 = 5 km/h. Step 2: Time = Distance ÷ Relative Speed = 20 ÷ 5 = 4 hours.

Question 17

A swimmer can swim at 6 km/h in still water. The river current flows at 2 km/h. If the swimmer swims 32 km upstream, how many hours will it take?

Accepted Answer

Step 1: Upstream speed = Speed of swimmer - Speed of current = 6 - 2 = 4 km/h. Step 2: Time = Distance ÷ Speed = 32 ÷ 4 = 8 hours.

Question 18

Two cyclists start from the same point and travel in opposite directions. Cyclist P travels at 18 km/h and Cyclist Q travels at 12 km/h. After how many minutes will they be 30 km apart?

Accepted Answer

Step 1: When moving in opposite directions, relative speed = 18 + 12 = 30 km/h. Step 2: Time = Distance ÷ Relative speed = 30 ÷ 30 = 1 hour. Step 3: Convert to minutes: 1 hour = 60 minutes.

Question 19

Two trains are moving towards each other on parallel tracks. Train A travels at 60 km/h and Train B travels at 40 km/h. If they are initially 300 km apart, in how many hours will they meet?

Accepted Answer

Step 1: When two objects move towards each other, their relative speed is the sum of their individual speeds. Step 2: Relative speed = 60 + 40 = 100 km/h. Step 3: Time = Distance ÷ Relative speed = 300 ÷ 100 = 3 hours.

Question 20

A boat travels at 20 km/h in still water. The speed of the current is 5 km/h. How long will it take the boat to travel 150 km downstream?

Accepted Answer

Step 1: Downstream speed = Speed of boat + Speed of current = 20 + 5 = 25 km/h. Step 2: Time = Distance ÷ Speed = 150 ÷ 25 = 6 hours.

Question 21

Two cyclists start from the same point and travel in opposite directions. Cyclist A travels at 12 km/h and Cyclist B travels at 8 km/h. How far apart will they be after 2.5 hours?

Accepted Answer

Step 1: When two objects travel in opposite directions, their relative speed is the sum of their individual speeds. Relative speed = 12 + 8 = 20 km/h. Step 2: Distance apart = Relative speed × Time = 20 × 2.5 = 50 km. Therefore, the answer is 50 km.

Question 22

A man cycles at 15 km/h and a boy runs at 5 km/h in the same direction on a straight road. If the man is initially 40 km behind the boy, after how many hours will the man catch up with the boy?

Accepted Answer

Step 1: When both move in the same direction, relative speed is the difference of their speeds. Relative speed = 15 − 5 = 10 km/h. Step 2: The man needs to cover the 40 km gap at this relative speed. Time = Distance ÷ Relative speed = 40 ÷ 10 = 4 hours. Therefore, the answer is 4 hours.

Question 23

Two trains are moving towards each other on parallel tracks. Train A travels at 60 km/h and Train B travels at 40 km/h. If they are currently 250 km apart, in how many hours will they meet?

Accepted Answer

Step 1: When two objects move towards each other, their relative speed is the sum of their individual speeds. Relative speed = 60 + 40 = 100 km/h. Step 2: Time = Distance ÷ Relative Speed = 250 ÷ 100 = 2.5 hours.

Question 24

A man cycles at 15 km/h and a woman cycles at 10 km/h in the same direction on the same road. If the woman starts 30 km ahead, how long will it take the man to catch up with the woman?

Accepted Answer

Step 1: When both move in the same direction, relative speed = difference of speeds = 15 - 10 = 5 km/h. Step 2: The man needs to cover the initial gap of 30 km at the relative speed. Step 3: Time = Distance ÷ Relative speed = 30 ÷ 5 = 6 hours.

Question 25

A man walks at 4 km/h and a woman walks at 6 km/h. They start from the same point and walk in the same direction. After 2 hours, how far apart will they be?

Accepted Answer

Step 1: When two people move in the same direction, relative speed is the difference of their speeds. Step 2: Relative speed = 6 − 4 = 2 km/h. Step 3: Distance apart = Relative speed × Time = 2 × 2 = 4 km.

Question 26

Two cyclists start from the same point and cycle in opposite directions. Cyclist A cycles at 15 km/h and Cyclist B at 25 km/h. After how many hours will they be 160 km apart?

Accepted Answer

Step 1: When two objects move in opposite directions, their relative speed is the sum of their individual speeds. Step 2: Relative speed = 15 + 25 = 40 km/h. Step 3: Time = Distance ÷ Relative speed = 160 ÷ 40 = 4 hours.

Question 27

A car is chasing a motorcycle on the same road. The car travels at 80 km/h and the motorcycle at 50 km/h. If the motorcycle has a head start of 90 km, how long will it take the car to catch up?

Accepted Answer

Step 1: When one object chases another in the same direction, relative speed is the difference of their speeds. Step 2: Relative speed = 80 − 50 = 30 km/h. Step 3: Time = Distance ÷ Relative speed = 90 ÷ 30 = 3 hours.

Question 28

Two trains are moving in the same direction at speeds of 72 km/h and 36 km/h. The faster train is 180 m long and the slower train is 120 m long. How long (in seconds) will the faster train take to cross the slower train completely?

Accepted Answer

Step 1: Relative speed (same direction) = 72 – 36 = 36 km/h. Step 2: Convert to m/s: 36 × (5/18) = 10 m/s. Step 3: Total distance to cover = length of both trains = 180 + 120 = 300 m. Step 4: Time = Distance / Relative Speed = 300 / 10 = 30 seconds. Therefore, the answer is 30 seconds.

NDA Relative Speed

NDA Relative Speed — Past Exam Questions

Relative Speed — Practice Questions