Question

Половину времени пути из одного города в другой автомобиль прошел со скоростью 60 км/ч. С какой скоростью он прошел остальное время если средняя скорость его равна 65 км/ч

Answer 1

Vcp = S/t , где S - весь путь, а t - всё время
t=t1+t2, из условия -> t=2*t1
теперь надо разобраться с S=s1+s2
s1=v1*t1
s2=v2*t1 (т к t1=t2), здесь v2 - искомая скорость
подставим всё в формулу
vcp=(v1*t1+v2*t1)/2t1 = t1*(v1+v2)/2t1 = (v1+v2)/2
2vcp = v1+v2
v2 = 2vcp-v1 = 2*65 - 60 = 70 км/ч
можно проще - сразу сказать, что vcp=(v1+v2)/2 и произвести дальнейшие вычисления

Answer 2

Solution:

Let's solve the problem step by step.

1. Calculate the distance: - We know that the average speed is 65 km/h and the first half of the distance is covered at 60 km/h. Using the formula: average speed = total distance / total time, we can calculate the total distance.

- The formula for average speed is: \[ \text{average speed} = \frac{\text{total distance}}{\text{total time}} \]

- Rearranging the formula to solve for total distance: \[ \text{total distance} = \text{average speed} \times \text{total time} \]

- Let's assume the total distance is \( D \) and the total time is \( T \). The first half of the distance is covered at 60 km/h, and the second half is covered at an unknown speed \( x \) km/h.

2. Calculate the time for each half: - The total time is the same for both halves of the journey. Let's denote the time taken for the first half as \( T_1 \) and the time taken for the second half as \( T_2 \).

- We can use the formula: \[ \text{time} = \frac{\text{distance}}{\text{speed}} \]

3. Formulate the equation: - We can set up an equation using the information we have to solve for the unknown speed \( x \).

4. Solve for the unknown speed: - Once we have the equation, we can solve for the unknown speed \( x \).

Calculation:

1. Calculate the distance: - Using the formula: \[ \text{total distance} = \text{average speed} \times \text{total time} \] - Given: average speed = 65 km/h - Let's assume the total distance is \( D \) and the total time is \( T \).

- Using the given information, we can calculate the total distance: \[ D = 65 \times T \]

2. Calculate the time for each half: - Let's denote the time taken for the first half as \( T_1 \) and the time taken for the second half as \( T_2 \). - We know that the first half of the distance is covered at 60 km/h, and the second half is covered at an unknown speed \( x \) km/h.

- Using the formula: \[ T_1 = \frac{D}{2 \times 60} \] \[ T_2 = \frac{D}{2 \times x} \]

3. Formulate the equation: - We know that the total time is the same for both halves of the journey. Therefore, \( T_1 = T_2 \). - We can set up an equation using the information we have to solve for the unknown speed \( x \).

- Equation: \[ \frac{D}{2 \times 60} = \frac{D}{2 \times x} \]

4. Solve for the unknown speed: - We can solve the equation to find the value of \( x \).

- Solving the equation: \[ \frac{D}{120} = \frac{D}{2x} \] \[ 2x = 120 \] \[ x = 60 \]

Answer:

The car covered the second half of the distance with a speed of 60 km/h.