Question

Расстояние между двумя городами 81 км Из них одновременно выехали два велосипедиста навстречу друг другу Скорость одного велосипедиста на 3 км в час больше другого Какое расстояние проехал каждый если встреча произошла через 3 часа

Answer 1

1) 81 : 3 = 27 (км/ч) - скорость сближения
2) (27 - 3) : 2 = 12 (км/ч) - скорость одного велосипедиста
3) 12 + 3 = 15 (км/ч) - скорость другого велосипедиста
4) 12 * 3 = 36 (км) - проехал первый велосипедист за 3 часа
5) 15 * 3 = 45 (км) - проехал второй велосипедист за 3 часа
Ответ: 36 км и 45 км.

Answer 2

Problem Analysis

We have two cyclists who start simultaneously from two different cities and are heading towards each other. The distance between the two cities is 81 km. One cyclist is traveling 3 km/h faster than the other. We need to determine the distance each cyclist has traveled when they meet after 3 hours.

Solution

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

To find the distance traveled by each cyclist, we can use the formula:

Distance = Speed × Time

For the slower cyclist: Distance1 = x km/h × 3 hours

For the faster cyclist: Distance2 = (x + 3) km/h × 3 hours

We know that the sum of the distances traveled by both cyclists should be equal to the total distance between the cities, which is 81 km.

Therefore, we can write the equation:

Distance1 + Distance2 = 81 km

Substituting the values of Distance1 and Distance2, we get:

x km/h × 3 hours + (x + 3) km/h × 3 hours = 81 km

Simplifying the equation:

3x + 3(x + 3) = 81

Solving for x:

6x + 9 = 81

6x = 72

x = 12

Now that we have the value of x, we can calculate the distances traveled by each cyclist.

For the slower cyclist: Distance1 = 12 km/h × 3 hours = 36 km

For the faster cyclist: Distance2 = (12 + 3) km/h × 3 hours = 15 km/h × 3 hours = 45 km

Answer

Therefore, the slower cyclist traveled 36 km and the faster cyclist traveled 45 km when they met after 3 hours.