Question

Мотоциклист проехал расстояние между двумя пунктами за 3 часа. Обратно он возвращался другой дорогой, которая короче первой на 7, 5 км. Увеличив скорость на 3 км/ч, он затратил на обратный путь 2 часа 30 минут. Найдите скорость движения мотоциклиста на обратном пути.

Answer 1

Пусть:

x - первое расстояние между городами

y-скорость на первом участке

y+3-скорость на втором участке

Тогда:

второе расстояние X-7.5

Составим и решим уравнение:

y+3 = (X-5)\2.5. y = x\3.

Подставляем , получаем (x+9)\3 = (x-7.5)\2.5.

Отсюда x=90-расстояние между городами. y=90\3=30км\ч

Скорость на обратной дороге = 33км\ч

Answer 2

Solution:

To find the speed of the motorcyclist on the return journey, we can use the formula: speed = distance / time

Let's denote: - d1 as the distance of the first journey - t1 as the time taken for the first journey - d2 as the distance of the second (return) journey - t2 as the time taken for the second (return) journey - s1 as the speed of the first journey - s2 as the speed of the return journey

We are given the following information: 1. The motorcyclist traveled the distance between two points in 3 hours. 2. On the return journey, he took 2 hours and 30 minutes, and the distance was 7.5 km shorter than the first journey. 3. He increased his speed by 3 km/h on the return journey.

We can set up the following equations based on the given information: 1. d1 = s1 * t1 2. d2 = s2 * t2 3. d2 = d1 - 7.5 4. s2 = s1 + 3 5. t1 = 3 hours 6. t2 = 2 hours and 30 minutes = 2.5 hours

Using these equations, we can solve for s2.

Calculation:

We know that: - d1 = s1 * t1 - d2 = s2 * t2 - d2 = d1 - 7.5 - s2 = s1 + 3 - t1 = 3 hours - t2 = 2.5 hours

From the given information, we can calculate: - d1 = s1 * 3 - d2 = (s1 + 3) * 2.5 - d2 = d1 - 7.5

Now, we can solve for s2 using the above equations.

Solution:

Substituting d1 = s1 * 3 into d2 = d1 - 7.5, we get: - (s1 + 3) * 2.5 = s1 * 3 - 7.5

Solving for s1: - 2.5s1 + 7.5 = 3s1 - 7.5 - 7.5 + 7.5 = 3s1 - 2.5s1 - 15 = 0.5s1 - s1 = 30 km/h

Therefore, the speed of the motorcyclist on the return journey (s2) is: - s2 = s1 + 3 - s2 = 30 + 3 - s2 = 33 km/h

So, the speed of the motorcyclist on the return journey is 33 km/h.