Tsd (Average Speed, Effective Speed)

Explanation
To find the average speed, we can use the formula: average speed = total distance / total time.

In this case, the total distance is the sum of the distances traveled at each speed. The distance traveled at 60 mph is 60 mph * 3 hours = 180 miles. The distance traveled at 24 mph is 24 mph * 5 hours = 120 miles. Therefore, the total distance is 180 miles + 120 miles = 300 miles.

The total time is the sum of the times traveled at each speed. The time traveled at 60 mph is 3 hours. The time traveled at 24 mph is 5 hours. Therefore, the total time is 3 hours + 5 hours = 8 hours.

Using the formula, average speed = total distance / total time, we get average speed = 300 miles / 8 hours = 37.5 mph.

Explanation
The average speed is calculated by taking the total distance traveled and dividing it by the total time taken. In this case, since the distance traveled in both directions is the same, the total distance is doubled. The time taken for the forward journey can be calculated by dividing the distance by the speed, and the same goes for the return journey. Adding these two times together gives the total time taken for the round trip. Dividing the total distance by the total time gives the average speed, which in this case is 37.5 kmph.

Explanation
The average speed from A to C can be found by taking the sum of the speeds from A to B and from B to C, and then dividing it by 2. This is because average speed is calculated by taking the total distance traveled and dividing it by the total time taken. In this case, since the time taken from A to B and from B to C is the same, the average speed is simply the sum of the speeds divided by 2.

Explanation
The swimmer covers a distance of 28 km against the current in 4 hours, which means his speed is 28/4 = 7 km/h. Similarly, he covers a distance of 40 km in the direction of the current in 4 hours, so his speed is 40/4 = 10 km/h. The speed of the current can be found by taking the difference between these two speeds, which is 10 - 7 = 3 km/h. However, the question asks for the speed of the current in kmph, so we need to convert this to kmph by dividing by the time taken, which is 4 hours. Therefore, the speed of the current is 3/4 = 0.75 kmph.

Explanation
The boat travels 2 km upstream, against the stream, and then returns downstream to the starting point in 30 minutes. Since the speed of the stream is 3 km/h, the boat's speed against the stream is reduced by 3 km/h. Let's assume the speed of the boat in still water is x km/h. So, the boat's speed against the stream is (x - 3) km/h, and the boat's speed downstream is (x + 3) km/h. The time taken to travel upstream is 2 / (x - 3) hours, and the time taken to travel downstream is 2 / (x + 3) hours. As given, the total time taken is 30 minutes, which is equal to 0.5 hours. Therefore, we can write the equation as: 2 / (x - 3) + 2 / (x + 3) = 0.5. Solving this equation, we find that x = 9. Hence, the speed of the boat in still water is 9 km/h.

Explanation
The boat takes longer to travel upstream than downstream, indicating that it is moving against the current of the stream. This means that the speed of the stream is subtracted from the speed of the boat when going upstream, causing the slower travel time. Conversely, when going downstream, the speed of the stream is added to the speed of the boat, resulting in a faster travel time. Since the boat's speed in still water is given as 4 km/h, the difference in travel time suggests that the speed of the stream is 2 km/h.

Explanation
The velocity of the stream can be found by taking the difference between the downstream speed and the upstream speed and dividing it by 2. In this case, the downstream speed is 30 kmph and the upstream speed is 10 kmph. The difference between these two speeds is 20 kmph. Dividing this by 2 gives us a velocity of the stream of 10 kmph.

Explanation
The concept of effective speed can be applied to boats and streams and escalators. In the case of boats and streams, the effective speed is the speed at which the boat is actually moving in still water, taking into account the speed of the stream. Similarly, in the case of escalators, the effective speed is the speed at which a person is actually moving on the escalator, taking into account the speed of the escalator itself. Therefore, the correct answer is only a and b.