Question

Велосипедист ехал из города в село со скоростью 3 км/ч, а возвращался со скоростью 5 км/ч. Найдите расстояние между селом и городом, если на весь путь он затратил 16ч? СРОЧНО ПОЖАЛУЙСТА​

Answer 1

Ответ:

..............................................

Answer 2

Problem Analysis

We are given that a cyclist traveled from a city to a village at a speed of 3 km/h and returned from the village to the city at a speed of 5 km/h. The total time taken for the entire journey was 16 hours. We need to find the distance between the village and the city.

Solution

Let's assume the distance between the village and the city is d km.

To find the distance, we can use the formula: distance = speed × time.

Let's calculate the time taken for the journey from the city to the village and from the village to the city.

The time taken from the city to the village can be calculated as: time1 = distance / speed1.

The time taken from the village to the city can be calculated as: time2 = distance / speed2.

According to the problem, the total time taken for the entire journey is 16 hours. So, we have the equation: time1 + time2 = 16.

Substituting the values, we get: distance / speed1 + distance / speed2 = 16.

Simplifying the equation, we get: distance × (1/speed1 + 1/speed2) = 16.

Now, let's substitute the given values into the equation and solve for the distance.

Calculation

Given: - Speed from city to village (speed1) = 3 km/h - Speed from village to city (speed2) = 5 km/h - Total time taken for the journey = 16 hours

Let's substitute the values into the equation and solve for the distance:

distance × (1/3 + 1/5) = 16

Simplifying the equation:

distance × (8/15) = 16

Dividing both sides of the equation by 8/15:

distance = 16 × (15/8)

distance = 30 km

Answer

The distance between the village and the city is 30 km.

Verification

Let's verify the answer using the given information.

The time taken from the city to the village can be calculated as: time1 = distance / speed1 = 30 km / 3 km/h = 10 hours.

The time taken from the village to the city can be calculated as: time2 = distance / speed2 = 30 km / 5 km/h = 6 hours.

The total time taken for the entire journey is time1 + time2 = 10 hours + 6 hours = 16 hours.

The calculated total time matches the given total time, which verifies that the answer is correct.

Therefore, the distance between the village and the city is 30 km.