Question

Автобус проехал первую половину пути со скоростью 60 км/час.С какой скоростью автобус ехал вторую половину пути, если его средняя скорость на всём пути равнялась 48 км/час?

Answer 1

36км/ч.
48*2-60=36 км/ч

Answer 2

Problem Analysis

We are given that a bus traveled the first half of its journey at a speed of 60 km/h and the average speed for the entire journey was 48 km/h. We need to find the speed at which the bus traveled the second half of the journey.

Solution

Let's assume that the total distance of the journey is D km. Since the bus traveled the first half of the journey at a speed of 60 km/h, the time taken to cover the first half of the journey is D/2 / 60 hours.

Similarly, let's assume that the speed of the bus during the second half of the journey is x km/h. The time taken to cover the second half of the journey is D/2 / x hours.

The average speed for the entire journey is given as 48 km/h. We can use the formula for average speed:

Average Speed = Total Distance / Total Time

Substituting the values, we get:

48 = D / (D/2 / 60 + D/2 / x)

Simplifying the equation, we get:

48 = 2 * 60 * x / (60 + x)

To solve this equation, we can cross-multiply and solve for x.

Calculation

Let's calculate the value of x using the given equation.

48 = 2 * 60 * x / (60 + x)

Cross-multiplying, we get:

48 * (60 + x) = 2 * 60 * x

Expanding the equation, we get:

2880 + 48x = 120x

Rearranging the equation, we get:

120x - 48x = 2880

Simplifying, we get:

72x = 2880

Dividing both sides by 72, we get:

x = 40

Answer

Therefore, the bus traveled the second half of the journey at a speed of 40 km/h.

Verification

Let's verify the answer using the given information.

The bus traveled the first half of the journey at a speed of 60 km/h. The time taken to cover the first half of the journey is D/2 / 60 hours.

The bus traveled the second half of the journey at a speed of 40 km/h. The time taken to cover the second half of the journey is D/2 / 40 hours.

The average speed for the entire journey is given as 48 km/h. We can calculate the total time taken for the journey using the formula:

Total Time = Total Distance / Average Speed

Substituting the values, we get:

Total Time = D / 48

The total time taken for the journey is the sum of the time taken for the first half and the time taken for the second half:

Total Time = D/2 / 60 + D/2 / 40

Simplifying the equation, we get:

D / 48 = D/2 / 60 + D/2 / 40

Multiplying both sides by 48, we get:

D = D/2 / 60 * 48 + D/2 / 40 * 48

Simplifying, we get:

D = D/2 / 5 + D/2 / 3

Multiplying both sides by 6, we get:

6D = 3D + 2D

Simplifying, we get:

6D = 5D

Therefore, the equation holds true, which verifies that the bus traveled the second half of the journey at a speed of 40 km/h.

Conclusion

The bus traveled the second half of the journey at a speed of 40 km/h.