Question

Из пункта А в пункт В, расстояние между которыми 200км, одновременно выезжают автомобиль и автобус. Скорость автомобиля на 60% больше скорости автобуса. Во время пути автомобиль делает получасовую остановку, но, несмотря на это, прибывает в пункт В на час раньше автобуса. С какой скоростью ехал автомобиль?Решите задачу, подробно напишите решение.

Answer 1

Скорость автомобиля x км/ч, что составляет 100%+60% = 160% от скорости автобуса. Тогда скорость автобуса

160% = x км/ч

100% = Vавт

Vавт = 100*x:160 = 0,625*x.

Автомобиль потратил на весь путь 200:x часов, автобус 200:0,625x, что на 1,5 часа больше (автомобиль делал получасовую остановку и прибыл на 1 час раньше). То есть

$\frac{200}{0,625x}-\frac{200}x=1,5\\ \frac{320}x-\farc{200}x=1,5\\ \frac{120}x=1,5\\ 1,5x=120\\ x=80$

Скорость автомобиля 80 км/ч.

Answer 2

Problem Analysis

We are given that a car and a bus start simultaneously from point A and travel a distance of 200 km to reach point B. The car's speed is 60% faster than the bus's speed. The car makes a 30-minute stop during the journey but still arrives at point B one hour earlier than the bus. We need to determine the speed of the car.

Solution

Let's assume the speed of the bus is x km/h. Therefore, the speed of the car is 1.6x km/h (60% faster than the bus).

To find the speed of the car, we can use the formula:

Speed = Distance / Time

We know that the distance is 200 km. Let's calculate the time taken by the bus and the car to travel this distance.

The time taken by the bus is given by:

Time taken by bus = Distance / Speed of bus

The time taken by the car is given by:

Time taken by car = Distance / Speed of car

We also know that the car makes a 30-minute (0.5 hours) stop during the journey. Therefore, the total time taken by the car is the sum of the time taken to travel the distance and the stoppage time:

Total time taken by car = Time taken by car + Stoppage time

Given that the car arrives at point B one hour earlier than the bus, we can write the equation:

Total time taken by car = Time taken by bus - 1 hour

Substituting the values, we get:

(Distance / Speed of car) + Stoppage time = (Distance / Speed of bus) - 1 hour

Simplifying the equation, we have:

(200 / (1.6x)) + 0.5 = (200 / x) - 1

Let's solve this equation to find the value of x.

Calculation

Let's solve the equation:

(200 / (1.6x)) + 0.5 = (200 / x) - 1

Multiplying both sides of the equation by (1.6x) to eliminate the denominators, we get:

200 + 0.8x = 320 - 1.6x

Adding 1.6x to both sides and subtracting 200 from both sides, we get:

2.4x = 120

Dividing both sides by 2.4, we get:

x = 50

Therefore, the speed of the bus is 50 km/h.

Since the speed of the car is 60% faster than the bus's speed, the speed of the car is:

Speed of car = 1.6 * 50 = 80 km/h

Answer

The car was traveling at a speed of 80 km/h.