Question

Помогите решить: От посёлка до станции мальчик дошёл за 0,4ч, а на обратный путь у него ушло на 0,15ч больше,так как средняя скорость его оказалась на 1,2 км/ч меньше. Определите расстояние от посёлка до станции

Answer 1

Пусть х км/ч - скорость почтальона от поселка до пристани,
х-1,2 км/ч- скорость от пристани до поселка. Так как на обратную дорогу он времени потратил больше на 0,15, то обратный путь он прошел за 0,4+0,15=0,55
Путь один и тот же, получаем ур-е
0,4х=0,55(х-1,2), решаем
0,4х-0,55х=-0,66
0,15х=0,66,
х=0,66/0,15=4,4 км/ч скорость почтальона от пристани до поселка.
4,4*0,4=1,76 км- путь от пристани до поселка.
ответ:1,76 км

Answer 2

Problem Analysis

We are given that a boy took 0.4 hours to walk from the village to the station, and on the return journey, it took him 0.15 hours longer because his average speed was 1.2 km/h less. We need to determine the distance from the village to the station.

Solution

Let's assume the distance from the village to the station is d kilometers.

We know that the time taken for the forward journey is 0.4 hours and the time taken for the return journey is 0.4 + 0.15 = 0.55 hours.

We can use the formula speed = distance / time to calculate the average speed for each journey.

For the forward journey: speed_forward = d / 0.4

For the return journey: speed_return = d / 0.55

We are also given that the average speed for the return journey is 1.2 km/h less than the average speed for the forward journey. So we can write the equation:

speed_return = speed_forward - 1.2

Now we can solve these equations to find the value of d.

Calculation

Let's substitute the values in the equations and solve for d.

From the equation speed_return = speed_forward - 1.2, we can substitute the values of speed_forward and speed_return:

(d / 0.55) = (d / 0.4) - 1.2

Now, let's solve this equation to find the value of d.

(d / 0.55) - (d / 0.4) = -1.2

To simplify the equation, we can multiply through by the least common multiple of the denominators, which is 0.22:

(0.22 * d / 0.55) - (0.22 * d / 0.4) = -1.2 * 0.22

Simplifying further:

(0.4 * d) - (0.55 * d) = -0.264

Combining like terms:

-0.15 * d = -0.264

Dividing both sides by -0.15:

d = -0.264 / -0.15

Calculating the value of d:

d = 1.76 kilometers

Answer

The distance from the village to the station is 1.76 kilometers.

Explanation

The boy took 0.4 hours to walk from the village to the station. On the return journey, it took him 0.15 hours longer because his average speed was 1.2 km/h less. By solving the equations, we found that the distance from the village to the station is 1.76 kilometers