Question

Расстояние между двумя городами 81 км. Из них навстречу друг другу выехали два велосипедиста. Один велосипедист проезжает в час на 3 км. больше другого . На каком расстоянии от городов они встретились , если встреча произошла чере 3 ч. после выезда. Помогите решить.

Answer 1

81 : 3 = 27 (км/ч) - скорость сближения(27 - 3) : 2 = 12 (км/ч) - скорость одного велосипедиста12 + 3 = 15 (км/ч) - скорость другого велосипедиста12 * 3 = 36 (км) - проехал первый велосипедист за 3 часа15 * 3 = 45 (км) - проехал второй велосипедист за 3 часаОтвет: 36 км и 45 км.

Answer 2

Problem Analysis

We have two cyclists who start from two different cities and meet each other after 3 hours. One cyclist travels 3 km per hour faster than the other. We need to find the distance at which they meet.

Solution

Let's assume the speed of the slower cyclist is x km/h. Therefore, the speed of the faster cyclist is (x + 3) km/h.

We know that distance = speed × time.

After 3 hours, the slower cyclist will have traveled a distance of 3x km (3 hours × x km/h), and the faster cyclist will have traveled a distance of 3(x + 3) km (3 hours × (x + 3) km/h).

Since they meet each other, the sum of their distances should be equal to the total distance between the two cities, which is 81 km.

So, we can set up the equation: 3x + 3(x + 3) = 81.

Simplifying the equation, we get: 6x + 9 = 81.

Subtracting 9 from both sides, we get: 6x = 72.

Dividing both sides by 6, we get: x = 12.

Now that we know the speed of the slower cyclist is 12 km/h, we can calculate the distance at which they meet.

The slower cyclist will have traveled a distance of 3x = 3 × 12 = 36 km, and the faster cyclist will have traveled a distance of 3(x + 3) = 3 × (12 + 3) = 45 km.

Therefore, they will meet at a distance of 36 km from one of the cities.

Answer

The two cyclists will meet at a distance of 36 km from one of the cities.

Explanation

Let's break down the solution step by step:

1. We assumed the speed of the slower cyclist as x km/h and the speed of the faster cyclist as (x + 3) km/h. 2. After 3 hours, the slower cyclist will have traveled a distance of 3x km and the faster cyclist will have traveled a distance of 3(x + 3) km. 3. We set up the equation 3x + 3(x + 3) = 81 to represent the sum of their distances being equal to the total distance between the cities. 4. Solving the equation, we found that x = 12. 5. Substituting the value of x, we calculated the distances traveled by each cyclist: 36 km for the slower cyclist and 45 km for the faster cyclist. 6. Therefore, they will meet at a distance of 36 km from one of the cities.

I hope this helps! Let me know if you have any further questions.