Question

Задача на 60 баллов З міста А в місто Б, відстань між якими дорівнює 300км., виїхав автобус. Через 20 хв йому на зустріч із Б в А виїхав автомобіль і через 2 год після виїзду зустрів автобус. З якою швидкістю їхав автомобіль, якщо відомо, що вона була на 20км\год більш швидкості автобуса. Нужно полное решение

Answer 1

Х км/ч - скорость автобуса
х + 20 км/ч - скорость автомобиля
20 минут = 1/3 часа

$\frac{1}{3}x+(x + x + 20) *2=300 \\ \\ \frac{1}{3}x+4x+40=300 \\ \\ x+2x+120=900 \\ \\ 13x=780$

х = 60 км/ч - скорость автобуса
60 + 20 = 80 км/ч - скорость автомобиля

Answer 2

Problem Analysis

We are given that a bus travels from city A to city B, a distance of 300 km. After 20 minutes, a car starts from city B towards city A and meets the bus after 2 hours. We need to find the speed of the car, knowing that it is 20 km/h faster than the bus.

Solution

Let's assume the speed of the bus is x km/h. Therefore, the speed of the car is (x + 20) km/h.

To find the solution, we can use the formula: speed = distance / time.

Let's calculate the time it takes for the bus to travel from city A to the meeting point with the car. Since the distance is 300 km and the speed is x km/h, the time is 300 / x hours.

Similarly, let's calculate the time it takes for the car to travel from city B to the meeting point with the bus. Since the distance is 300 km and the speed is (x + 20) km/h, the time is 300 / (x + 20) hours.

According to the problem, the car starts 20 minutes (1/3 hour) after the bus. Therefore, the time it takes for the car to reach the meeting point is (300 / (x + 20)) - (1/3) hours.

We are given that the car reaches the meeting point 2 hours after it starts. Therefore, we can set up the equation:

(300 / (x + 20)) - (1/3) = 2

Let's solve this equation to find the value of x, which represents the speed of the bus.

Calculation

To solve the equation, we can start by multiplying both sides by (x + 20) to eliminate the denominator:

300 - (1/3)(x + 20) = 2(x + 20)

Next, we can simplify the equation:

300 - (1/3)x - (20/3) = 2x + 40

Combining like terms:

(1/3)x + 2x = 300 - 40 + (20/3)

Simplifying further:

(7/3)x = 260 + (20/3)

To get rid of the fraction, we can multiply both sides by 3:

7x = 780 + 20

7x = 800

Finally, we can solve for x by dividing both sides by 7:

x = 800 / 7

Calculating the value of x:

x ≈ 114.29 km/h

Therefore, the speed of the car is approximately (114.29 + 20) km/h = 134.29 km/h.

Answer

The car was traveling at a speed of approximately 134.29 km/h.

Please note that this solution assumes constant speeds for both the bus and the car throughout their journeys.