Speed, Time and Distance

The average speed for a round trip when the distances are equal is given by the harmonic mean formula: Average speed = 2 × (speed1 × speed2) / (speed1 + speed2). Here, the man travels 2 km at 6 km/hr and returns 2 km at 4 km/hr. Applying the formula: 2 × (6 × 4) / (6 + 4) = 48 / 10 = 4.8 km/hr. Therefore, the correct average speed is 4.8 km/hr, which corresponds to option B.

Let the usual time be T. Walking at 5/6 speed means time taken is T × (6/5) = 1.2T. The delay is 40 minutes, so 1.2T - T = 40 minutes ⇒ 0.2T = 40 ⇒ T = 200 minutes = 3 hours 20 minutes. Hence, option A is correct.

The average speed is calculated by dividing the total distance by the total time. Total distance = 160 + 160 = 320 km. Time for first part = 160/64 = 2.5 hours; time for second part = 160/80 = 2 hours. Total time = 4.5 hours. Average speed = 320/4.5 ≈ 71.11 km/hr, which corresponds to option C. However, the calculation shows 71.11 km/hr, so option C is correct. The original correct_answer was C, but option D is 72.21 km/hr which is incorrect. Therefore, the original correct_answer C is correct, but option B has a typo with an extra space. The explanation was missing and is now added. Difficulty is medium because it requires calculation of average speed over different speeds.

The train's speed is 60 km/hr, which converts to 16.67 m/s (60 × 1000 / 3600 or 60 × 5/18). The time to pass a pole equals the length of the train divided by its speed: 125 m / 16.67 m/s ≈ 7.5 seconds. Therefore, the correct answer is option C (7.5s).

Yalmaz's speed = 400 m / 120 s = 10/3 m/s. Rayan's speed = 1000 m / 300 s = 10/3 m/s. Both speeds are equal, so the ratio is 1:1. However, checking the calculations carefully: Yalmaz's speed = 400/120 = 3.33 m/s, Rayan's speed = 1000/300 = 3.33 m/s, so the ratio is indeed 1:1. The original correct answer was D (1:1), which is correct. The options are correct, but option B (4:3) is incorrect. Therefore, the correct answer remains D.

The boatman's speed in still water is 7 km/hr and the river speed is 3 km/hr. Upstream speed = 7 - 3 = 4 km/hr, downstream speed = 7 + 3 = 10 km/hr. Let the distance be d km. Time difference is 6 hours: d/4 - d/10 = 6. Solving gives d = 40 km.

To find the speed in km/h, convert the distance and time to compatible units. Distance = 600 meters = 0.6 kilometers. Time = 5 minutes = 5/60 hours = 1/12 hours. Speed = distance/time = 0.6 km / (1/12) hours = 0.6 * 12 = 7.2 km/h. Therefore, the correct answer is option D (7.2 km/h).

Let the total distance be x km. The man travels half the distance (x/2) at 21 km/hr and the other half (x/2) at 24 km/hr. Total time = (x/2)/21 + (x/2)/24 = 10 hours. Solving for x gives x = 112 km.

The speed of the train is 54 km/hr, which converts to 15 m/s. The train passes a man in 20 seconds, so the length of the train is speed × time = 15 m/s × 20 s = 300 m. The train passes the platform in 36 seconds, so the total distance covered is 15 m/s × 36 s = 540 m. The length of the platform is the total distance minus the length of the train, which is 540 m - 300 m = 240 m. Therefore, the correct answer is 240 meters (option C).

The relative speed of the train with respect to the jogger is (45 - 9) = 36 kmph, which converts to 10 m/s. The total distance to be covered for the train to pass the jogger is the sum of the initial gap and the train length: 240 + 120 = 360 meters. Time = distance/speed = 360/10 = 36 seconds.

The train's speed is 240 m / 24 s = 10 m/s. To pass a platform 650 m long, the train must cover 240 + 650 = 890 m. Time taken = 890 m / 10 m/s = 89 seconds, which rounds to 89 seconds. However, option B is 89 Sec, so the correct answer is B, not C. Rechecking: 890/10=89 seconds exactly, so correct answer is B.

When two trains move in opposite directions, their relative speed is the sum of their speeds: 60 + 90 = 150 km/hr. Converting to m/s: 150 × (1000/3600) = 41.67 m/s. The total length to be crossed is 1.10 + 0.9 = 2.0 km = 2000 m. Time taken = distance / speed = 2000 / 41.67 ≈ 48 seconds. However, the question asks for the time taken by the slower train to cross the faster train, which is the same as the time for them to completely pass each other, so 48 seconds is correct. But the options given are 36, 45, 48, and 49, and the original correct answer was C (48). The calculation confirms 48 seconds is correct, so the original correct answer C is correct. The explanation was missing and is now provided. Difficulty is medium due to calculation complexity.

The lorry's speed is 100 km divided by 2.5 hours, which equals 40 km/h. The car's speed is given as 55 km/h. Therefore, the ratio of their speeds is 40:55, which simplifies to 8:11. Since option A is 8:11, it matches the correct ratio. However, the options given do not include 8:11 as option B is 20:11 and option A is 8:11. The correct answer is A, not B.