Question

Мотоцикл расчитал, что если он будет ехать из поселка до станции со скоростью 32 км/ч, то приедет на станцию на 30 мин до отхода поезда. Однако из-за ненастной погоды он ехал со скоростью на 7 меньшей и поэтому опоздал к поезду на 12 мин. Чему равно расстояние от поселка до станции?

Answer 1

Пусть х время которое должен был потратить мотоцикл от посёлка до станции, но опоздал на 30+12=42 мин.=0,07 ч., т.к ехал 32-7=25 км/ч. 
32х=25(х+0,7) 
32х=25х+17,5
7х=17,5
х=2,5 часа должен был потратить мотоцикл от посёлка до станции.
32×2,5=80 км расстояние от поселка до станции.
Ответ: 80 км.

Answer 2

Calculation of Distance from Village to Station

To calculate the distance from the village to the station, we can use the information provided about the motorcycle's speed and the time it takes to reach the station under normal conditions and with the delay caused by bad weather.

Let's break down the given information:

- The motorcycle calculated that if it travels from the village to the station at a speed of 32 km/h, it will arrive at the station 30 minutes before the train's departure. - However, due to bad weather, the motorcycle traveled at a speed 7 km/h slower than usual and arrived at the station 12 minutes late.

To find the distance from the village to the station, we can set up an equation using the formula:

Distance = Speed × Time

Let's denote the distance as 'd', the normal speed as 's', and the time taken under normal conditions as 't'.

From the given information, we can set up the following equations:

Equation 1: d = s × t (1)

Equation 2: d = (s - 7) × (t + 12/60) (2)

We can solve these equations simultaneously to find the values of 'd', 's', and 't'.

Solving the Equations

To solve the equations, we can use substitution. Rearrange Equation 2 to solve for 't':

(s - 7) × (t + 12/60) = s × t

Simplifying the equation:

s × t - 7t + 12/60 × (s - 7) = s × t

- 7t + 12/60 × (s - 7) = 0

- 7t + (1/5) × (s - 7) = 0

- 7t + (s/5) - 7/5 = 0

- 7t + s/5 = 7/5

- 35t + s = 7

t = (s - 7)/35 (3)

Substitute Equation 3 into Equation 1:

d = s × [(s - 7)/35] (4)

Simplifying Equation 4:

d = (s^2 - 7s)/35

Now, we can substitute the given values into Equation 4 to find the distance 'd'.

Calculation

Given: - Speed under normal conditions: 32 km/h - Delay caused by bad weather: 12 minutes - Speed reduction due to bad weather: 7 km/h

Substituting the values into Equation 4:

d = ((32)^2 - 7 × 32)/35

d = (1024 - 224)/35

d = 800/35

d ≈ 22.857 km

Therefore, the distance from the village to the station is approximately 22.857 kilometers.

Please note that the above calculation assumes a linear relationship between speed and time, which may not be entirely accurate in real-world scenarios. Additionally, the given information does not specify the units of time used (minutes or hours). However, based on the given context, it is assumed that the time is in minutes.