Question

Задача. Автомобіль проїхав 500 км. Відомо, що першу половину всього шляху він рухався зі швидкістю 100 км/год, а другу половину шляху проїхав на 30 хв швидше. Якою була швидкість руху автомобіля на другій ділянці шляху? Рух автомобіля вважайте рівномірним.

Answer 1

Ответ:

125 км/год.

Объяснение:

Перша половина шляху, яку автомобіль проїхав зі швидкістю 100 км/год, складає 500/2 = 250 км.

Друга половина шляху складає також 250 км.

За час T, який потрібний для проїзду першої половини шляху, відстань дорівнює швидкості, помноженій на час: 250 = 100*T.

Отже, T = 250/100 = 2,5 години.

Згідно умови, другу половину шляху автомобіль проїхав на 30 хвилин (0,5 години) швидше, ніж першу половину.

Тому, час для другої половини шляху становить 2,5 - 0,5 = 2 години.

Відстань для другої половини шляху дорівнює швидкості, помноженій на час: 250 = V * 2.

Отже, швидкість для другої ділянки шляху дорівнює 250 / 2 = 125 км/год.

Думаю понятно написала

Answer 2

Problem Analysis

To solve this problem, we need to find the speed at which the car traveled on the second half of the journey. We are given that the car traveled a total distance of 500 km, and the first half of the journey was covered at a speed of 100 km/h. Additionally, we know that the second half of the journey was completed 30 minutes faster than the first half. We need to determine the speed of the car during the second half of the journey.

Solution

Let's assume that the speed of the car during the second half of the journey is x km/h.

We know that the first half of the journey was covered at a speed of 100 km/h. Therefore, the time taken to cover the first half of the journey can be calculated using the formula:

Time = Distance / Speed

For the first half of the journey, the distance is 250 km (half of the total distance) and the speed is 100 km/h. Substituting these values into the formula, we get:

Time1 = 250 km / 100 km/h

Now, we are given that the second half of the journey was completed 30 minutes faster than the first half. Since the time taken for the second half of the journey is less than the time taken for the first half, we can subtract 30 minutes from the time taken for the first half:

Time2 = Time1 - 30 minutes

To convert the 30 minutes to hours, we divide by 60:

Time2 = Time1 - 30/60 hours

Now, we can calculate the time taken for the second half of the journey using the formula:

Time = Distance / Speed

For the second half of the journey, the distance is also 250 km (half of the total distance) and the speed is x km/h. Substituting these values into the formula, we get:

Time2 = 250 km / x km/h

Since we know that Time2 = Time1 - 30/60 hours, we can equate the two expressions for Time2:

250 km / x km/h = Time1 - 30/60 hours

Now, we can substitute the value of Time1 into the equation:

250 km / x km/h = (250 km / 100 km/h) - 30/60 hours

Simplifying the equation, we get:

250 / x = 250 / 100 - 0.5

Now, we can solve for x by cross-multiplying and simplifying the equation:

250 * 100 = 250 * x - 0.5 * x

25000 = 250x - 0.5x

25000 = 249.5x

x = 25000 / 249.5

x ≈ 100.40

Therefore, the speed of the car during the second half of the journey was approximately 100.40 km/h.

Answer

The speed of the car during the second half of the journey was approximately 100.40 km/h.