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

Х-скорость автобуса, 120/х+0,4- его время
х+10-скорость автомобиля, 120/х+10-время
120/х+0,4-120/х+10=1
120х+1200+0,4x^2+4x-120x-x^2-10x=0
-0,6x^2-6x+1200=0
x^2+10x-2000=0
x=40, x=-50-не удов.усл.
Ответ: скорость автобуса 40км/ч

Answer 2

Problem Analysis

We are given that the distance from the city to the village is 120 km. An bus leaves the city and after an hour, a car leaves the city following the bus. The car's speed is 10 km/h faster than the bus. We need to find the speed of the bus if both the car and the bus arrive 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 know that the time taken by both the bus and the car to travel from the city to the village is the same. Let's denote this time as t hours.

The distance traveled by the bus in time t is 120 km. The distance traveled by the car in time t is also 120 km.

Using the formula distance = speed × time, we can write the following equations:

For the bus: 120 = x × t For the car: 120 = (x + 10) × t We also know that the bus made a stop for 24 minutes, which is equivalent to 24/60 = 0.4 hours. Therefore, the total time taken by the bus is t + 0.4 hours.

Substituting the value of t from equation into equation we can solve for x.

Calculation

Let's solve the equations to find the value of x:

From equation 120 = x × t

From equation 120 = (x + 10) × t

Substituting the value of t from equation into equation 120 = (x + 10) × (120 / x)

Simplifying the equation: 120 = 120 + 1200/x

Subtracting 120 from both sides: 0 = 1200/x

Since the left side of the equation is 0, the right side must also be 0. Therefore, 1200/x = 0.

Solving for x: 1200 = 0

Since the equation 1200 = 0 is not possible, it means that there is no solution for the given problem. The values provided in the problem statement are not consistent.

Answer

There is no solution for the given problem. The values provided in the problem statement are not consistent.