Question

Половину пути велосипедист проехал со скоростью 12 км/ч, остальной путь — со скоростью 4 км/ч. С какой средней скоростью нужно было ехать велосипедисту, чтобы на весь путь затратить такое же количество времени? Дайте ответ в километрах в час.

Answer 1

Т.е. время одинаковы, значит средняя скорость будет
$v_c= \frac{v_1+v_2}{2} = \frac{12+4}{2}=8$ км/ч

Ответ: 8 км/ч.

Answer 2

Problem Analysis

A cyclist travels half of the distance at a speed of 12 km/h and the remaining distance at a speed of 4 km/h. We need to find the average speed at which the cyclist should have traveled in order to spend the same amount of time for the entire journey.

Solution

Let's assume the total distance traveled by the cyclist is D km.

The time taken to travel the first half of the distance at a speed of 12 km/h can be calculated using the formula: Time1 = Distance1 / Speed1

Similarly, the time taken to travel the second half of the distance at a speed of 4 km/h can be calculated using the formula: Time2 = Distance2 / Speed2

Since the total time taken for the entire journey is the same, we can equate Time1 and Time2: Time1 = Time2

Substituting the formulas for Time1 and Time2, we get: Distance1 / Speed1 = Distance2 / Speed2

We know that Distance1 + Distance2 = D, so we can rewrite the equation as: Distance1 / Speed1 = (D - Distance1) / Speed2

Simplifying the equation, we get: Distance1 * Speed2 = (D - Distance1) * Speed1

Expanding the equation, we get: Distance1 * Speed2 = D * Speed1 - Distance1 * Speed1

Rearranging the equation, we get: Distance1 * (Speed2 + Speed1) = D * Speed1

Finally, we can calculate the average speed at which the cyclist should have traveled using the formula: Average Speed = Total Distance / Total Time

Since the total distance is D and the total time is D / Average Speed, we can substitute these values into the formula to get: Average Speed = D / (D / Average Speed)

Simplifying the equation, we get: Average Speed = Average Speed

This means that the average speed at which the cyclist should have traveled is equal to the average speed itself. Therefore, the average speed is 12 km/h.

Answer

The cyclist should have traveled at an average speed of 12 km/h in order to spend the same amount of time for the entire journey.