Question 1

A train 200 metres long passes another train 150 metres long, moving in the same direction. The first train travels at 60 km/h and the second train travels at 40 km/h. How long will it take for the first train to completely pass the second train?

Accepted Answer

Step 1: When two trains pass each other in the same direction, the total distance to be covered is the sum of their lengths: 200 + 150 = 350 metres. Step 2: Convert speeds to m/s: 60 km/h = 60 × (5/18) = 16.67 m/s and 40 km/h = 40 × (5/18) = 11.11 m/s. Step 3: Relative speed = 16.67 − 11.11 = 5.56 m/s. Step 4: Time = 350 ÷ 5.56 ≈ 63 seconds. Alternatively, use relative speed in km/h: 60 − 40 = 20 km/h. Convert 350 m to km: 0.35 km. Time = 0.35 ÷ 20 = 0.0175 hours = 63 seconds. Therefore, the answer is 63 seconds.

Question 2

A train travels 240 km in 4 hours at a constant speed. What is the speed of the train in km/h?

Accepted Answer

Step 1: Use the formula Speed = Distance ÷ Time. Step 2: Speed = 240 ÷ 4 = 60 km/h. Therefore, the answer is 60 km/h.

Question 3

Train A travels at 72 km/h. How long will it take to cover 360 km?

Accepted Answer

Step 1: Use the formula Time = Distance ÷ Speed. Step 2: Time = 360 ÷ 72 = 5 hours. Therefore, the answer is 5 hours.

Question 4

Two trains start from the same station at the same time. Train X travels at 48 km/h and Train Y travels at 60 km/h in the same direction. After 3 hours, what is the distance between them?

Accepted Answer

Step 1: Calculate distance covered by Train X: 48 × 3 = 144 km. Step 2: Calculate distance covered by Train Y: 60 × 3 = 180 km. Step 3: Distance between them = 180 − 144 = 36 km. Therefore, the answer is 36 km.

Question 5

A train 150 metres long passes a stationary pole in 10 seconds. What is the speed of the train in m/s?

Accepted Answer

Step 1: When a train passes a pole, the distance covered equals the length of the train. Step 2: Use Speed = Distance ÷ Time. Step 3: Speed = 150 ÷ 10 = 15 m/s. Therefore, the answer is 15 m/s.

Question 6

Train P and Train Q are moving towards each other on parallel tracks. Train P travels at 50 km/h and Train Q travels at 40 km/h. If they are initially 270 km apart, in how many hours will they meet?

Accepted Answer

Step 1: When two trains move towards each other, their relative speed is the sum of their individual speeds. Step 2: Relative speed = 50 + 40 = 90 km/h. Step 3: Use Time = Distance ÷ Relative Speed. Step 4: Time = 270 ÷ 90 = 3 hours. Therefore, the answer is 3 hours.

Question 7

Train A and Train B are running in the same direction on parallel tracks. Train A is 200 metres long and travels at 80 km/h. Train B is 150 metres long and travels at 60 km/h. How much time (in seconds) will it take for Train A to completely overtake Train B?

Accepted Answer

Step 1: Convert speeds to m/s. Train A: 80 × (5/18) = 22.22 m/s (approximately 200/9 m/s). Train B: 60 × (5/18) = 16.67 m/s (approximately 50/3 m/s). Step 2: Since both trains move in the same direction, relative speed = 80 - 60 = 20 km/h = 20 × (5/18) = 50/9 m/s ≈ 5.56 m/s. Step 3: For Train A to completely overtake Train B, it must cover a distance equal to the sum of both train lengths = 200 + 150 = 350 metres. Step 4: Time = Distance ÷ Relative speed = 350 ÷ (50/9) = 350 × (9/50) = 63 seconds.

Question 8

Train A and Train B are running on parallel tracks. Train A is 240 metres long and crosses a stationary pole in 12 seconds. Train B is 180 metres long and crosses the same pole in 9 seconds. How much time (in seconds) will it take for the two trains to completely pass each other when running in opposite directions?

Accepted Answer

Step 1: Speed of Train A = 240 ÷ 12 = 20 m/s. Step 2: Speed of Train B = 180 ÷ 9 = 20 m/s. Step 3: When trains move in opposite directions, relative speed = 20 + 20 = 40 m/s. Step 4: Total distance to cover = 240 + 180 = 420 metres. Step 5: Time = 420 ÷ 40 = 10.5 seconds.

Question 9

Train X crosses a 150-metre platform in 18 seconds and a 250-metre platform in 26 seconds. What is the speed of Train X (in km/h)?

Accepted Answer

Step 1: Let the length of Train X = L metres and speed = S m/s. Step 2: When crossing a platform, distance = train length + platform length. Step 3: For 150 m platform: L + 150 = S × 18 ... (equation 1). Step 4: For 250 m platform: L + 250 = S × 26 ... (equation 2). Step 5: Subtract equation 1 from equation 2: (L + 250) - (L + 150) = 26S - 18S → 100 = 8S → S = 12.5 m/s. Step 6: Convert to km/h: 12.5 × (18/5) = 12.5 × 3.6 = 45 km/h.

Question 10

Two trains start simultaneously from stations A and B, which are 480 km apart. Train P travels from A to B at 60 km/h, while Train Q travels from B to A at 40 km/h. After how many hours will they meet?

Accepted Answer

Step 1: When two objects move towards each other, their relative speed = sum of individual speeds. Step 2: Relative speed = 60 + 40 = 100 km/h. Step 3: Distance between stations = 480 km. Step 4: Time to meet = Distance ÷ Relative speed = 480 ÷ 100 = 4.8 hours.

Question 11

A train 320 metres long is running at 45 km/h. A man standing on a platform watches the train pass. How long does it take for the entire train to pass the man (in seconds)?

Accepted Answer

Step 1: Convert speed from km/h to m/s: 45 km/h = 45 × (5/18) = 12.5 m/s. Step 2: When a train passes a stationary man (point object), the distance covered = length of the train = 320 metres. Step 3: Time = Distance ÷ Speed = 320 ÷ 12.5 = 25.6 seconds.

Question 12

A train 150 metres long crosses a platform 250 metres long in 20 seconds. Another train 120 metres long travels at twice the speed of the first train. How long will the second train take to cross the same platform?

Accepted Answer

Step 1: For the first train, total distance to cross = train length + platform length = 150 + 250 = 400 metres. Step 2: Speed of first train = 400 ÷ 20 = 20 m/s. Step 3: Speed of second train = 2 × 20 = 40 m/s. Step 4: Distance for second train to cross = 120 + 250 = 370 metres. Step 5: Time = 370 ÷ 40 = 9.25 seconds. Therefore, the answer is 9.25 seconds.

Question 13

Two trains start from the same station at the same time. Train P travels towards the north at 72 km/h, while Train Q travels towards the south at 48 km/h. After how much time will they be 360 km apart?

Accepted Answer

Step 1: Since the trains travel in opposite directions (north and south), their relative speed = 72 + 48 = 120 km/h. Step 2: Time to be 360 km apart = Distance ÷ Relative speed = 360 ÷ 120 = 3 hours. Therefore, the answer is 3 hours.

Question 14

Train A and Train B start simultaneously from stations P and Q respectively, which are 480 km apart. Train A travels towards Q at 60 km/h, while Train B travels towards P at 40 km/h. At what time will they meet, and how far will Train A have travelled by then?

Accepted Answer

Step 1: When two trains travel 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 A = Speed × Time = 60 × 4.8 = 288 km. Therefore, the answer is 4.8 hours and 288 km.

Question 15

A train travels from City A to City B, a distance of 360 km. For the first 120 km, it travels at 60 km/h. For the next 180 km, it travels at 90 km/h. For the remaining distance, it travels at 120 km/h. What is the average speed of the train for the entire journey?

Accepted Answer

Step 1: Segment 1: Distance = 120 km, Speed = 60 km/h, Time = 120 ÷ 60 = 2 hours. Step 2: Segment 2: Distance = 180 km, Speed = 90 km/h, Time = 180 ÷ 90 = 2 hours. Step 3: Segment 3: Distance = 360 - 120 - 180 = 60 km, Speed = 120 km/h, Time = 60 ÷ 120 = 0.5 hours. Step 4: Total time = 2 + 2 + 0.5 = 4.5 hours. Step 5: Average speed = Total distance ÷ Total time = 360 ÷ 4.5 = 80 km/h. Therefore, the answer is 80 km/h.

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