Question

Расстояние от города до посёлка равно 120 км. Из города в посёлок выехал автобус. Через час после этого вслед за ним выехал автомобиль, скорость которого на 10 км/ч больше скорости автобуса. Найдите скорость автобуса (в км/ч), если известно, что в пути он сделал остановку на 24 минуты, а в посёлок автомобиль и автобус прибыли одновременно.

Answer 1

Problem Analysis

We are given that the distance from the city to the village is 120 km. An bus leaves the city and an hour later, a car leaves the city with a speed that is 10 km/h faster than the bus. We need to find the speed of the bus if we know that the bus made a 24-minute stop during the journey and both the car and the bus arrived at the village at the same time.

Solution

Let's assume the speed of the bus is x km/h. Since the car's speed is 10 km/h faster than the bus, the speed of the car is (x + 10) km/h.

We can calculate the time it takes for the bus to travel from the city to the village using the formula:

time = distance / speed

The time taken by the bus is given by:

time_bus = (120 km) / (x km/h)

Since the car left an hour after the bus, the time taken by the car is:

time_car = (120 km) / ((x + 10) km/h)

We know that the car and the bus arrived at the village at the same time. Therefore, the total time taken by the bus (including the 24-minute stop) should be equal to the time taken by the car:

time_bus + 24 minutes = time_car

Converting 24 minutes to hours:

24 minutes = 24/60 hours = 0.4 hours

Substituting the values, we get:

(120 km) / (x km/h) + 0.4 hours = (120 km) / ((x + 10) km/h)

Simplifying the equation:

120 / x + 0.4 = 120 / (x + 10)

To solve this equation, we can cross-multiply:

120(x + 10) = (120 / x) * (x + 10)

Simplifying further:

120x + 1200 = 120(x + 10)

Expanding:

120x + 1200 = 120x + 1200

We can see that the equation is an identity, which means that the value of x (the speed of the bus) can be any real number. Therefore, the speed of the bus cannot be determined based on the given information.

Answer

The speed of the bus cannot be determined based on the given information.