Context: A bus covers the first half of a total distance with a speed of 50 m/s and then covers the second half of the distance with a speed of 60 m/s.  Find the average speed of the bus over the entire trip. Answer question

The average speed of a journey is calculated by the total distance travelled divided by the total time taken. In this case, the bus travels the same distance (let's call it D) twice at different speeds.

1. First, calculate the time taken for each half of the journey. Time is distance divided by speed. So for the first half, the time is D/50 and for the second half, the time is D/60.

2. Add these times together to get the total time taken for the journey. So the total time is D/50 + D/60.

3. The total distance travelled is 2D (since the bus travels distance D twice).

4. Now, calculate the average speed by dividing the total distance by the total time. So the average speed is 2D / (D/50 + D/60).

5. Simplify this equation to find the average speed. The D's cancel out, and you can find a common denominator for the fractions to get 2 / (1/50 + 1/60).

6. Simplify further to get the average speed = 2 / (110/3000) = 2 * (3000/110) = 6000/110 = 54.55 m/s.

So the average speed of the bus over the entire trip is approximately 54.55 m/s.