Question

Автобус и грузовая машина, скорость которой на 16 км/ч больше скорости автобуса, выехали одновременно навстречу друг другу из двух городов, расстояние между которыми 438 км. Найди скорости автобуса и грузовой машины, если известно, что они встретились через 3 ч. после выезда.

Answer 1

Скорость пешехода - 3кмч
1) 3*4=12 (кмч) - скорость велосипедиста
2) 3*3=9(км) - прошел пешеход за 3 часа
3) 12*3=36 (км) - проехал за 3 часа велосипедист
4) 36+9=45 (км) - расстояние от села до села
Ответ: расстояние от первого села до второго равно 45 километров

Answer 2

Problem Analysis

We are given that a bus and a truck, whose speed is 16 km/h greater than the speed of the bus, start from two cities and travel towards each other. The distance between the cities is 438 km. They meet after 3 hours. We need to find the speeds of the bus and the truck.

Solution

Let's assume the speed of the bus is x km/h. Since the speed of the truck is 16 km/h greater than the speed of the bus, the speed of the truck is x + 16 km/h.

We know that the distance traveled by both the bus and the truck is the same, which is 438 km.

The time taken by the bus to cover this distance is given by the formula: time = distance / speed. Therefore, the time taken by the bus is 438 / x hours.

Similarly, the time taken by the truck is 438 / (x + 16) hours.

According to the problem, the bus and the truck meet after 3 hours. Therefore, the sum of the time taken by the bus and the time taken by the truck is equal to 3 hours.

Mathematically, we can express this as:

438 / x + 438 / (x + 16) = 3

To solve this equation, we can multiply both sides by x(x + 16) to eliminate the denominators:

438(x + 16) + 438x = 3x(x + 16)

Simplifying this equation will give us the value of x, which represents the speed of the bus. We can then calculate the speed of the truck by adding 16 to the speed of the bus.

Let's solve this equation to find the speeds of the bus and the truck.

Calculation

438(x + 16) + 438x = 3x(x + 16)

Expanding the equation:

438x + 7008 + 438x = 3x^2 + 48x

Combining like terms:

876x + 7008 = 3x^2 + 48x

Rearranging the equation:

3x^2 + 48x - 876x - 7008 = 0

Simplifying:

3x^2 - 828x - 7008 = 0

Using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

where a = 3, b = -828, and c = -7008.

Solving for x:

x = (-(-828) ± √((-828)^2 - 4 * 3 * -7008)) / (2 * 3)

Simplifying:

x = (828 ± √(685584 + 84192)) / 6

x = (828 ± √(769776)) / 6

x = (828 ± 876) / 6

Simplifying further:

x = (828 + 876) / 6 or x = (828 - 876) / 6

x = 1704 / 6 or x = -48 / 6

x = 284 or x = -8

Since speed cannot be negative, we can discard the negative value. Therefore, the speed of the bus is 284 km/h.

The speed of the truck is 16 km/h greater than the speed of the bus, so the speed of the truck is 284 + 16 = 300 km/h.

Answer

The speed of the bus is 284 km/h and the speed of the truck is 300 km/h.