Question

Из А в В одновременно выехали два автомобиля. Первый проехал с постоянной скоростью весь путь. Второй проехал первую половину пути со скоростью 60 км/ч , а вторую половину пути — со скоростью, на 18 км/ч большей скорости первого, в результате чего прибыл в В одновременно с первым автомобилем. Найдите скорость первого автомобиля. Ответ дайте в км/ч.

Answer 1

х - скорость первого автомобиля (постоянная)

х = 0,5 * 60 + 0,5 * (х + 18)

х = 30 + 0,5х + 9 

х - 0,5х = 30 + 9

0,5х = 39

х =  39 :  0,5

х = 78 (км/ч) - скорость первого автомобиля

Проверка: 0,5 * 60 + 0,5 * (78 + 18) = 30 + 48 = 78 (км/ч) - средняя скорость второго

                   78 = 78 - верно. 

Answer 2

Problem Analysis

We are given that two cars, A and B, simultaneously start from point A and travel to point B. The first car travels the entire distance at a constant speed, while the second car travels the first half of the distance at a speed of 60 km/h and the second half at a speed 18 km/h faster than the first car. We need to find the speed of the first car.

Solution

Let's assume the distance between points A and B is d km.

The time taken by the first car to travel from A to B is given by: Time taken by first car = Distance / Speed of first car = d / Speed of first car (Equation 1)

The time taken by the second car to travel the first half of the distance is given by: Time taken by second car for first half = Distance / Speed of second car for first half = d/2 / 60 km/h = d/120 hours (Equation 2)

The time taken by the second car to travel the second half of the distance is given by: Time taken by second car for second half = Distance / Speed of second car for second half = d/2 / (Speed of first car + 18 km/h) (Equation 3)

Since the second car arrives at point B at the same time as the first car, the total time taken by the second car is equal to the time taken by the first car: Time taken by second car = Time taken by first car (Equation 4)

Substituting the values from equations 1, 2, and 3 into equation 4, we get: d/120 + d/2 / (Speed of first car + 18 km/h) = d / Speed of first car (Equation 5)

Simplifying equation 5, we get: d/120 + d/2 / (Speed of first car + 18 km/h) - d / Speed of first car = 0

To solve this equation, we can multiply through by the least common multiple of the denominators, which is 120 * (Speed of first car + 18 km/h) * Speed of first car: d * (Speed of first car + 18 km/h) + 60d - 120d = 0

Simplifying further, we get: d * (Speed of first car + 18 km/h) - 60d = 0

Factoring out d, we get: d * (Speed of first car + 18 km/h - 60) = 0

Since d cannot be zero, we can solve for Speed of first car + 18 km/h - 60 = 0: Speed of first car + 18 km/h - 60 = 0

Simplifying, we get: Speed of first car + 18 km/h = 60

Finally, solving for Speed of first car, we subtract 18 km/h from both sides: Speed of first car = 60 km/h - 18 km/h = 42 km/h

Therefore, the speed of the first car is 42 km/h.

Answer

The speed of the first car is 42 km/h.